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Номер 922, страница 252 - гдз по алгебре 9 класс учебник Солтан, Солтан
Авторы: Солтан Г. Н., Солтан А. Е., Жумадилова А. Ж.
Тип: Учебник
Издательство: Кокшетау
Год издания: 2019 - 2026
ISBN: 978-601-317-424-2
Рекомендовано Министерством образования и науки Республики Казахстан
Популярные ГДЗ в 9 классе
Повторение курса алгебры 7-9 классов. Уравнения, неравенства и их системы - номер 922, страница 252.
App\Models\Task {#1030 // resources/views/models/task/default.blade.php #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1108677 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "252" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-922" "field_display_title" => "922" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037 #items: array:1 [ 0 => App\Models\Term {#1036 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #original: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1035 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1071 #items: array:1 [ 0 => App\Models\Branch {#1034 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1107678 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Повторение курса алгебры 7-9 классов" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "249" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1038 #items: array:1 [ 0 => App\Models\Book {#1040 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 4298 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1041 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1043 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1045 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1047 #items: array:3 [ …3] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1051 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1052 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1054 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1056 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1058 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1059 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1060 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1061 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1062 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1063 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для учащихся 9 класса общеобразовательных школ" "field_allowed" => "Рекомендовано Министерством образования и науки Республики Казахстан" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1291" "field_priority" => "4" "field_default_folder" => "/algebra_09/soltan-u19/" "field_isbn" => "978-601-317-424-2" "field_cover" => array:1 [ 0 => "/media/algebra_09/soltan-u19/covers/cover1.webp?ts=1752140452" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ …4] ] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1064 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1065 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1066 #items: [] #escapeWhenCastingToString: false } "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1067 #items: [] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 380 "subject" => 542 "class_subject" => 386 ] ] #original: array:50 [ "id" => 4298 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1041} "field_class" => Illuminate\Database\Eloquent\Collection {#1043} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1045} "field_author" => Illuminate\Database\Eloquent\Collection {#1047} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1051} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1052} "field_country" => Illuminate\Database\Eloquent\Collection {#1054} "field_city" => Illuminate\Database\Eloquent\Collection {#1056} "field_series" => Illuminate\Database\Eloquent\Collection {#1058} "field_umk" => Illuminate\Database\Eloquent\Collection {#1059} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1060} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1061} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1062} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1063} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для учащихся 9 класса общеобразовательных школ" "field_allowed" => "Рекомендовано Министерством образования и науки Республики Казахстан" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1291" "field_priority" => "4" "field_default_folder" => "/algebra_09/soltan-u19/" "field_isbn" => "978-601-317-424-2" "field_cover" => array:1 [ 0 => "/media/algebra_09/soltan-u19/covers/cover1.webp?ts=1752140452" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ …4] ] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1064} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1065} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1066} "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1067} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 380 "subject" => 542 "class_subject" => 386 ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1068 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1107678 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Повторение курса алгебры 7-9 классов" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039} "field_page_start" => "249" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1038} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1068} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1104 #items: array:2 [ 0 => App\Models\Branch {#1112 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1107678 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Повторение курса алгебры 7-9 классов" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1113 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "249" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1144 #items: array:1 [ 0 => App\Models\Book {#1114 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 4298 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1116 #items: array:1 [ 0 => App\Models\Term {#1115 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6471 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Алгебра" "field_abbreviated_name" => null "field_cases" => array:6 [ "field_accusative_case" => "алгебру" "field_creative_case" => "алгеброй" "field_dative_case" => "алгебре" "field_genitive_case" => "алгебры" "field_nominative_case" => "алгебра" "field_prepositional_case" => "алгебре" ] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "algebra" ] #original: array:10 [ "id" => 6471 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Алгебра" "field_abbreviated_name" => null "field_cases" => array:6 [ "field_accusative_case" => "алгебру" "field_creative_case" => "алгеброй" "field_dative_case" => "алгебре" "field_genitive_case" => "алгебры" "field_nominative_case" => "алгебра" "field_prepositional_case" => "алгебре" ] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "algebra" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1117 #items: array:1 [ 0 => App\Models\Term {#1118 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5458 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "9" "field_cases" => array:6 [ "field_accusative_case" => "девятый" "field_creative_case" => "девятым" "field_dative_case" => "девятому" "field_genitive_case" => "девятого" "field_nominative_case" => "девятый" "field_prepositional_case" => "девятом" ] "field_translit" => "devjatyj" ] #original: array:6 [ "id" => 5458 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "9" "field_cases" => array:6 [ "field_accusative_case" => "девятый" "field_creative_case" => "девятым" "field_dative_case" => "девятому" "field_genitive_case" => "девятого" "field_nominative_case" => "девятый" "field_prepositional_case" => "девятом" ] "field_translit" => "devjatyj" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1119 #items: array:1 [ 0 => App\Models\Term {#1120 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 7002 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Кокшетау" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "Kokshetau" ] #original: array:6 [ "id" => 7002 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Кокшетау" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "Kokshetau" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1121 #items: array:3 [ 0 => App\Models\Term {#1122 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 7003 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Солтан" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Генадий" "field_patronymic" => "Николаевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 7003 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Солтан" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Генадий" "field_patronymic" => "Николаевич" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Term {#1123 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 7004 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Солтан" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Алла" "field_patronymic" => "Евгеньевна" "field_surname_rp" => null ] #original: array:12 [ "id" => 7004 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Солтан" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Алла" "field_patronymic" => "Евгеньевна" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Term {#1124 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 7005 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Жумадилова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Аманбала" "field_patronymic" => "Жумадиловна" "field_surname_rp" => null ] #original: array:12 [ "id" => 7005 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Жумадилова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Аманбала" "field_patronymic" => "Жумадиловна" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1125 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1126 #items: array:1 [ 0 => App\Models\Term {#1127 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6671 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Учебник" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "учебник" "field_creative_case" => "учебником" "field_dative_case" => "учебнику" "field_genitive_case" => "учебника" "field_nominative_case" => "учебник" "field_prepositional_case" => "учебнике" ] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "uchebnik" ] #original: array:10 [ "id" => 6671 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Учебник" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "учебник" "field_creative_case" => "учебником" "field_dative_case" => "учебнику" "field_genitive_case" => "учебника" "field_nominative_case" => "учебник" "field_prepositional_case" => "учебнике" ] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "uchebnik" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1128 #items: array:1 [ 0 => App\Models\Term {#1129 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 6994 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Казахстан" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "kazakhstan" ] #original: array:6 [ "id" => 6994 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Казахстан" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "kazakhstan" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1130 #items: array:1 [ 0 => App\Models\Term {#1131 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 6995 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Алматы" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "almaty" ] #original: array:6 [ "id" => 6995 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Алматы" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "almaty" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1132 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1133 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1134 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1135 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1136 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1137 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для учащихся 9 класса общеобразовательных школ" "field_allowed" => "Рекомендовано Министерством образования и науки Республики Казахстан" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1291" "field_priority" => "4" "field_default_folder" => "/algebra_09/soltan-u19/" "field_isbn" => "978-601-317-424-2" "field_cover" => array:1 [ 0 => "/media/algebra_09/soltan-u19/covers/cover1.webp?ts=1752140452" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/algebra_09/soltan-u19/covers/cover1.webp?ts=1752140452" "alt" => "" "width" => "1940" "height" => "2895" ] ] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1138 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1139 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1140 #items: [] #escapeWhenCastingToString: false } "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1141 #items: [] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 380 "subject" => 542 "class_subject" => 386 ] ] #original: array:50 [ "id" => 4298 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1116} "field_class" => Illuminate\Database\Eloquent\Collection {#1117} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1119} "field_author" => Illuminate\Database\Eloquent\Collection {#1121} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1125} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1126} "field_country" => Illuminate\Database\Eloquent\Collection {#1128} "field_city" => Illuminate\Database\Eloquent\Collection {#1130} "field_series" => Illuminate\Database\Eloquent\Collection {#1132} "field_umk" => Illuminate\Database\Eloquent\Collection {#1133} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1134} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1135} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1136} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1137} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для учащихся 9 класса общеобразовательных школ" "field_allowed" => "Рекомендовано Министерством образования и науки Республики Казахстан" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1291" "field_priority" => "4" "field_default_folder" => "/algebra_09/soltan-u19/" "field_isbn" => "978-601-317-424-2" "field_cover" => array:1 [ 0 => "/media/algebra_09/soltan-u19/covers/cover1.webp?ts=1752140452" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/algebra_09/soltan-u19/covers/cover1.webp?ts=1752140452" "alt" => "" "width" => "1940" "height" => "2895" ] ] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1138} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1139} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1140} "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1141} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 380 "subject" => 542 "class_subject" => 386 ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1142 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1107678 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Повторение курса алгебры 7-9 классов" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1113} "field_page_start" => "249" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1144} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1142} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Branch {#1143 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1107680 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Уравнения, неравенства и их системы" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1145 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "252" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1146 #items: array:1 [ 0 => App\Models\Book {#1114} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1147 #items: array:1 [ 0 => App\Models\Branch {#1034} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1107680 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Уравнения, неравенства и их системы" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1145} "field_page_start" => "252" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1146} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1147} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1096 #items: array:3 [ 0 => App\Models\Element {#1085 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 1277277 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1076 #items: array:1 [ 0 => App\Models\Edition {#1086 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 4953 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1080 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "pasha" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1083 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1082 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1081 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 4953 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1080} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "pasha" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1083} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1082} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1081} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1108677" "type" => "task" ] "text" => "<p><strong>922.</strong> Решите уравнение:</p><p><strong>a)</strong> $\frac{5x^2 - x}{x} = 1$;</p><p><strong>б)</strong> $\frac{x^2 - x}{x - 3} = \frac{6}{x - 3}$;</p><p><strong>в)</strong> $\frac{5}{2 + 3x} + \frac{3x}{3x - 2} = \frac{8}{9x^2 - 4}$.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "922-1.jpg" "alt" => null "width" => "1121" "height" => 386 "path" => "/media/algebra_09/soltan-u19/0-1/922-1.webp?ts=1752834899" ] ] ] #original: array:7 [ "id" => 1277277 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1076} "task" => array:2 [ "refs" => "1108677" "type" => "task" ] "text" => "<p><strong>922.</strong> Решите уравнение:</p><p><strong>a)</strong> $\frac{5x^2 - x}{x} = 1$;</p><p><strong>б)</strong> $\frac{x^2 - x}{x - 3} = \frac{6}{x - 3}$;</p><p><strong>в)</strong> $\frac{5}{2 + 3x} + \frac{3x}{3x - 2} = \frac{8}{9x^2 - 4}$.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "922-1.jpg" "alt" => null "width" => "1121" "height" => 386 "path" => "/media/algebra_09/soltan-u19/0-1/922-1.webp?ts=1752834899" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Element {#1078 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1278568 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1107 #items: array:1 [ 0 => App\Models\Edition {#1079 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 4954 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1074 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Неизвестный" "field_moderator" => "pasha" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1075 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1072 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1103 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 4954 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1074} "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Неизвестный" "field_moderator" => "pasha" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1075} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1072} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1103} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1108677" "type" => "task" ] "img" => array:2 [ 0 => array:5 [ "name" => "922-1.jpg" "alt" => null "width" => "1312" "height" => 2412 "path" => "/media/algebra_09/soltan-u19/1-1/922-1.webp?ts=1752831740" ] 1 => array:5 [ "name" => "922-2.jpg" "alt" => null "width" => "1233" "height" => 511 "path" => "/media/algebra_09/soltan-u19/1-1/922-2.webp?ts=1752831740" ] ] ] #original: array:6 [ "id" => 1278568 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1107} "task" => array:2 [ "refs" => "1108677" "type" => "task" ] "img" => array:2 [ 0 => array:5 [ "name" => "922-1.jpg" "alt" => null "width" => "1312" "height" => 2412 "path" => "/media/algebra_09/soltan-u19/1-1/922-1.webp?ts=1752831740" ] 1 => array:5 [ "name" => "922-2.jpg" "alt" => null "width" => "1233" "height" => 511 "path" => "/media/algebra_09/soltan-u19/1-1/922-2.webp?ts=1752831740" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Element {#1102 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1554523 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1152 #items: array:1 [ 0 => App\Models\Edition {#1111 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 5665 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 2 (rus)" "field_order" => "3" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1108 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "2-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1106 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1148 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1149 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 5665 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 2 (rus)" "field_order" => "3" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1108} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "2-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1106} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1148} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1149} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1108677" "type" => "task" ] "text" => "<p><strong>а)</strong></p><p>Исходное уравнение: $ \frac{5x^2 - x}{x} = 1 $.</p><p>Область допустимых значений (ОДЗ): знаменатель не должен быть равен нулю, следовательно, $x \neq 0$.</p><p>Умножим обе части уравнения на $x$, чтобы избавиться от знаменателя:</p><p>$5x^2 - x = 1 \cdot x$</p><p>$5x^2 - x = x$</p><p>Перенесем все члены в левую часть:</p><p>$5x^2 - x - x = 0$</p><p>$5x^2 - 2x = 0$</p><p>Вынесем общий множитель $x$ за скобки:</p><p>$x(5x - 2) = 0$</p><p>Произведение равно нулю, когда хотя бы один из множителей равен нулю. Получаем два возможных решения:</p><p>1) $x = 0$</p><p>2) $5x - 2 = 0 \implies 5x = 2 \implies x = \frac{2}{5}$</p><p>Проверим полученные корни по ОДЗ. Корень $x=0$ не удовлетворяет условию $x \neq 0$, поэтому он является посторонним. Корень $x = \frac{2}{5}$ удовлетворяет ОДЗ.</p><p><strong>Ответ:</strong> $ \frac{2}{5} $</p><p><strong>б)</strong></p><p>Исходное уравнение: $ \frac{x^2 - x}{x - 3} = \frac{6}{x - 3} $.</p><p>ОДЗ: знаменатель не должен быть равен нулю, следовательно, $x - 3 \neq 0$, то есть $x \neq 3$.</p><p>Поскольку знаменатели дробей в обеих частях уравнения равны, мы можем приравнять их числители (при условии, что $x$ входит в ОДЗ):</p><p>$x^2 - x = 6$</p><p>Перенесем все члены в левую часть, чтобы получить стандартное квадратное уравнение:</p><p>$x^2 - x - 6 = 0$</p><p>Решим это уравнение. Можно использовать теорему Виета. Сумма корней равна 1, а их произведение равно -6. Подбором находим корни:</p><p>$x_1 = 3$</p><p>$x_2 = -2$</p><p>Проверим корни по ОДЗ. Корень $x_1 = 3$ не удовлетворяет условию $x \neq 3$, значит, это посторонний корень. Корень $x_2 = -2$ удовлетворяет ОДЗ.</p><p><strong>Ответ:</strong> -2</p><p><strong>в)</strong></p><p>Исходное уравнение: $ \frac{5}{2 + 3x} + \frac{3x}{3x - 2} = \frac{8}{9x^2 - 4} $.</p><p>ОДЗ: все знаменатели должны быть не равны нулю.</p><p>1) $2 + 3x \neq 0 \implies 3x \neq -2 \implies x \neq -\frac{2}{3}$</p><p>2) $3x - 2 \neq 0 \implies 3x \neq 2 \implies x \neq \frac{2}{3}$</p><p>3) $9x^2 - 4 \neq 0$. Разложим знаменатель по формуле разности квадратов: $(3x)^2 - 2^2 = (3x - 2)(3x + 2)$. Значит, $(3x - 2)(3x + 2) \neq 0$, что дает те же ограничения: $x \neq \frac{2}{3}$ и $x \neq -\frac{2}{3}$.</p><p>Общий знаменатель для всех дробей: $9x^2 - 4 = (3x - 2)(3x + 2)$. Приведем все дроби к общему знаменателю.</p><p>$ \frac{5(3x - 2)}{(3x + 2)(3x - 2)} + \frac{3x(3x + 2)}{(3x - 2)(3x + 2)} = \frac{8}{(3x - 2)(3x + 2)} $</p><p>Умножим обе части уравнения на общий знаменатель $(3x - 2)(3x + 2)$, при условии $x \neq \pm \frac{2}{3}$:</p><p>$5(3x - 2) + 3x(3x + 2) = 8$</p><p>Раскроем скобки:</p><p>$15x - 10 + 9x^2 + 6x = 8$</p><p>Приведем подобные слагаемые и запишем уравнение в стандартном виде:</p><p>$9x^2 + (15x + 6x) - 10 - 8 = 0$</p><p>$9x^2 + 21x - 18 = 0$</p><p>Разделим все уравнение на 3 для упрощения:</p><p>$3x^2 + 7x - 6 = 0$</p><p>Решим квадратное уравнение через дискриминант $D = b^2 - 4ac$:</p><p>$D = 7^2 - 4 \cdot 3 \cdot (-6) = 49 + 72 = 121 = 11^2$</p><p>Найдем корни:</p><p>$x_1 = \frac{-b + \sqrt{D}}{2a} = \frac{-7 + 11}{2 \cdot 3} = \frac{4}{6} = \frac{2}{3}$</p><p>$x_2 = \frac{-b - \sqrt{D}}{2a} = \frac{-7 - 11}{2 \cdot 3} = \frac{-18}{6} = -3$</p><p>Проверим корни по ОДЗ. Корень $x_1 = \frac{2}{3}$ не удовлетворяет условию $x \neq \frac{2}{3}$, поэтому является посторонним. Корень $x_2 = -3$ удовлетворяет ОДЗ.</p><p><strong>Ответ:</strong> -3</p>" ] #original: array:6 [ "id" => 1554523 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1152} "task" => array:2 [ "refs" => "1108677" "type" => "task" ] "text" => "<p><strong>а)</strong></p><p>Исходное уравнение: $ \frac{5x^2 - x}{x} = 1 $.</p><p>Область допустимых значений (ОДЗ): знаменатель не должен быть равен нулю, следовательно, $x \neq 0$.</p><p>Умножим обе части уравнения на $x$, чтобы избавиться от знаменателя:</p><p>$5x^2 - x = 1 \cdot x$</p><p>$5x^2 - x = x$</p><p>Перенесем все члены в левую часть:</p><p>$5x^2 - x - x = 0$</p><p>$5x^2 - 2x = 0$</p><p>Вынесем общий множитель $x$ за скобки:</p><p>$x(5x - 2) = 0$</p><p>Произведение равно нулю, когда хотя бы один из множителей равен нулю. Получаем два возможных решения:</p><p>1) $x = 0$</p><p>2) $5x - 2 = 0 \implies 5x = 2 \implies x = \frac{2}{5}$</p><p>Проверим полученные корни по ОДЗ. Корень $x=0$ не удовлетворяет условию $x \neq 0$, поэтому он является посторонним. Корень $x = \frac{2}{5}$ удовлетворяет ОДЗ.</p><p><strong>Ответ:</strong> $ \frac{2}{5} $</p><p><strong>б)</strong></p><p>Исходное уравнение: $ \frac{x^2 - x}{x - 3} = \frac{6}{x - 3} $.</p><p>ОДЗ: знаменатель не должен быть равен нулю, следовательно, $x - 3 \neq 0$, то есть $x \neq 3$.</p><p>Поскольку знаменатели дробей в обеих частях уравнения равны, мы можем приравнять их числители (при условии, что $x$ входит в ОДЗ):</p><p>$x^2 - x = 6$</p><p>Перенесем все члены в левую часть, чтобы получить стандартное квадратное уравнение:</p><p>$x^2 - x - 6 = 0$</p><p>Решим это уравнение. Можно использовать теорему Виета. Сумма корней равна 1, а их произведение равно -6. Подбором находим корни:</p><p>$x_1 = 3$</p><p>$x_2 = -2$</p><p>Проверим корни по ОДЗ. Корень $x_1 = 3$ не удовлетворяет условию $x \neq 3$, значит, это посторонний корень. Корень $x_2 = -2$ удовлетворяет ОДЗ.</p><p><strong>Ответ:</strong> -2</p><p><strong>в)</strong></p><p>Исходное уравнение: $ \frac{5}{2 + 3x} + \frac{3x}{3x - 2} = \frac{8}{9x^2 - 4} $.</p><p>ОДЗ: все знаменатели должны быть не равны нулю.</p><p>1) $2 + 3x \neq 0 \implies 3x \neq -2 \implies x \neq -\frac{2}{3}$</p><p>2) $3x - 2 \neq 0 \implies 3x \neq 2 \implies x \neq \frac{2}{3}$</p><p>3) $9x^2 - 4 \neq 0$. Разложим знаменатель по формуле разности квадратов: $(3x)^2 - 2^2 = (3x - 2)(3x + 2)$. Значит, $(3x - 2)(3x + 2) \neq 0$, что дает те же ограничения: $x \neq \frac{2}{3}$ и $x \neq -\frac{2}{3}$.</p><p>Общий знаменатель для всех дробей: $9x^2 - 4 = (3x - 2)(3x + 2)$. Приведем все дроби к общему знаменателю.</p><p>$ \frac{5(3x - 2)}{(3x + 2)(3x - 2)} + \frac{3x(3x + 2)}{(3x - 2)(3x + 2)} = \frac{8}{(3x - 2)(3x + 2)} $</p><p>Умножим обе части уравнения на общий знаменатель $(3x - 2)(3x + 2)$, при условии $x \neq \pm \frac{2}{3}$:</p><p>$5(3x - 2) + 3x(3x + 2) = 8$</p><p>Раскроем скобки:</p><p>$15x - 10 + 9x^2 + 6x = 8$</p><p>Приведем подобные слагаемые и запишем уравнение в стандартном виде:</p><p>$9x^2 + (15x + 6x) - 10 - 8 = 0$</p><p>$9x^2 + 21x - 18 = 0$</p><p>Разделим все уравнение на 3 для упрощения:</p><p>$3x^2 + 7x - 6 = 0$</p><p>Решим квадратное уравнение через дискриминант $D = b^2 - 4ac$:</p><p>$D = 7^2 - 4 \cdot 3 \cdot (-6) = 49 + 72 = 121 = 11^2$</p><p>Найдем корни:</p><p>$x_1 = \frac{-b + \sqrt{D}}{2a} = \frac{-7 + 11}{2 \cdot 3} = \frac{4}{6} = \frac{2}{3}$</p><p>$x_2 = \frac{-b - \sqrt{D}}{2a} = \frac{-7 - 11}{2 \cdot 3} = \frac{-18}{6} = -3$</p><p>Проверим корни по ОДЗ. Корень $x_1 = \frac{2}{3}$ не удовлетворяет условию $x \neq \frac{2}{3}$, поэтому является посторонним. Корень $x_2 = -3$ удовлетворяет ОДЗ.</p><p><strong>Ответ:</strong> -3</p>" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1108678" "type" => "task" ] "previous" => array:2 [ "refs" => "1108676" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1090 #items: array:1 [ 0 => App\Models\Book {#1114} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1070 #items: array:1 [ 0 => App\Models\BookPage {#1100 #connection: "mysql" #table: "book_pages" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 1097994 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "252" "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/page-252" "field_display_title" => "252" "field_folder" => "folder1" "field_image_name" => "252" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1073 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1095 #items: array:1 [ 0 => App\Models\Book {#1114} ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "edition_groups" => Illuminate\Database\Eloquent\Collection {#1097 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1154 #items: array:1 [ 0 => App\Models\Element {#1153 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1261145 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1155 #items: array:1 [ …1] #escapeWhenCastingToString: false } "book_page" => array:2 [ "refs" => "1097994" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ …5] ] ] #original: array:6 [ "id" => 1261145 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1155} "book_page" => array:2 [ "refs" => "1097994" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ …5] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1097995" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1097993" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1479 #items: array:8 [ 0 => App\Models\Task {#1493 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1108674 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "252" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-919" "field_display_title" => "919" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1494 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1495 #items: [] …1 } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1496 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1565 …2} "content" => Illuminate\Database\Eloquent\Collection {#1575 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1582 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1108674 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "252" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-919" "field_display_title" => "919" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1494} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1495 …1} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1496 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1565 …2} "content" => Illuminate\Database\Eloquent\Collection {#1575 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1582 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Task {#1567 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1108675 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "252" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-920" "field_display_title" => "920" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1568 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1566 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1573 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1572 …2} "content" => Illuminate\Database\Eloquent\Collection {#1570 …2} "next" => array:2 [ …2] "previous" => 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"field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1579 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1580 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1581 …2} "content" => Illuminate\Database\Eloquent\Collection {#1574 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1602 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1108676 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "252" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-921" "field_display_title" => "921" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1571 …2} "field_metatags_title" => null "field_metatags_description" => null 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"field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1612 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1613 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1614 …2} "content" => Illuminate\Database\Eloquent\Collection {#1624 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1631 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1108678 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "252" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-923" "field_display_title" => "923" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1611 …2} "field_metatags_title" => null "field_metatags_description" => null 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#perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1108679 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "252" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-924" "field_display_title" => "924" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1617 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1616 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1622 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1621 …2} "content" => Illuminate\Database\Eloquent\Collection {#1619 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => 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Illuminate\Database\Eloquent\Collection {#1626 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 6 => App\Models\Task {#1618 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1108680 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "252" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-925" "field_display_title" => "925" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1620 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1628 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1629 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1630 …2} "content" => Illuminate\Database\Eloquent\Collection {#1623 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1651 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1108680 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "252" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-925" "field_display_title" => "925" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1620 …2} "field_metatags_title" => null "field_metatags_description" => null 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Illuminate\Database\Eloquent\Collection {#1665 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1108681 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "252" "field_page_end" => "253" "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-926" "field_display_title" => "926" "field_outside_task" => "0" "field_task_type" => Illuminate\Database\Eloquent\Collection {#1625 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1650 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1652 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1648 …2} "content" => Illuminate\Database\Eloquent\Collection {#1647 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1665 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:21 [ "id" => 1097994 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "252" "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/page-252" "field_display_title" => "252" "field_folder" => "folder1" "field_image_name" => "252" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1073} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1095} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "edition_groups" => Illuminate\Database\Eloquent\Collection {#1097} "content" => Illuminate\Database\Eloquent\Collection {#1154} "next" => array:2 [ "refs" => "1097995" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1097993" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1479} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1108677 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "252" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-922" "field_display_title" => "922" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1035} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1071} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1104} "content" => Illuminate\Database\Eloquent\Collection {#1096} "next" => array:2 [ "refs" => "1108678" "type" => "task" ] "previous" => array:2 [ "refs" => "1108676" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1090} "page" => array:2 [ "refs" => "1097994" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] }
№922 (с. 252)
Условие. №922 (с. 252)
скриншот условия
922. Решите уравнение:
a) $\frac{5x^2 - x}{x} = 1$;
б) $\frac{x^2 - x}{x - 3} = \frac{6}{x - 3}$;
в) $\frac{5}{2 + 3x} + \frac{3x}{3x - 2} = \frac{8}{9x^2 - 4}$.
Решение. №922 (с. 252)
Решение 2 (rus). №922 (с. 252)
а)
Исходное уравнение: $ \frac{5x^2 - x}{x} = 1 $.
Область допустимых значений (ОДЗ): знаменатель не должен быть равен нулю, следовательно, $x \neq 0$.
Умножим обе части уравнения на $x$, чтобы избавиться от знаменателя:
$5x^2 - x = 1 \cdot x$
$5x^2 - x = x$
Перенесем все члены в левую часть:
$5x^2 - x - x = 0$
$5x^2 - 2x = 0$
Вынесем общий множитель $x$ за скобки:
$x(5x - 2) = 0$
Произведение равно нулю, когда хотя бы один из множителей равен нулю. Получаем два возможных решения:
1) $x = 0$
2) $5x - 2 = 0 \implies 5x = 2 \implies x = \frac{2}{5}$
Проверим полученные корни по ОДЗ. Корень $x=0$ не удовлетворяет условию $x \neq 0$, поэтому он является посторонним. Корень $x = \frac{2}{5}$ удовлетворяет ОДЗ.
Ответ: $ \frac{2}{5} $
б)
Исходное уравнение: $ \frac{x^2 - x}{x - 3} = \frac{6}{x - 3} $.
ОДЗ: знаменатель не должен быть равен нулю, следовательно, $x - 3 \neq 0$, то есть $x \neq 3$.
Поскольку знаменатели дробей в обеих частях уравнения равны, мы можем приравнять их числители (при условии, что $x$ входит в ОДЗ):
$x^2 - x = 6$
Перенесем все члены в левую часть, чтобы получить стандартное квадратное уравнение:
$x^2 - x - 6 = 0$
Решим это уравнение. Можно использовать теорему Виета. Сумма корней равна 1, а их произведение равно -6. Подбором находим корни:
$x_1 = 3$
$x_2 = -2$
Проверим корни по ОДЗ. Корень $x_1 = 3$ не удовлетворяет условию $x \neq 3$, значит, это посторонний корень. Корень $x_2 = -2$ удовлетворяет ОДЗ.
Ответ: -2
в)
Исходное уравнение: $ \frac{5}{2 + 3x} + \frac{3x}{3x - 2} = \frac{8}{9x^2 - 4} $.
ОДЗ: все знаменатели должны быть не равны нулю.
1) $2 + 3x \neq 0 \implies 3x \neq -2 \implies x \neq -\frac{2}{3}$
2) $3x - 2 \neq 0 \implies 3x \neq 2 \implies x \neq \frac{2}{3}$
3) $9x^2 - 4 \neq 0$. Разложим знаменатель по формуле разности квадратов: $(3x)^2 - 2^2 = (3x - 2)(3x + 2)$. Значит, $(3x - 2)(3x + 2) \neq 0$, что дает те же ограничения: $x \neq \frac{2}{3}$ и $x \neq -\frac{2}{3}$.
Общий знаменатель для всех дробей: $9x^2 - 4 = (3x - 2)(3x + 2)$. Приведем все дроби к общему знаменателю.
$ \frac{5(3x - 2)}{(3x + 2)(3x - 2)} + \frac{3x(3x + 2)}{(3x - 2)(3x + 2)} = \frac{8}{(3x - 2)(3x + 2)} $
Умножим обе части уравнения на общий знаменатель $(3x - 2)(3x + 2)$, при условии $x \neq \pm \frac{2}{3}$:
$5(3x - 2) + 3x(3x + 2) = 8$
Раскроем скобки:
$15x - 10 + 9x^2 + 6x = 8$
Приведем подобные слагаемые и запишем уравнение в стандартном виде:
$9x^2 + (15x + 6x) - 10 - 8 = 0$
$9x^2 + 21x - 18 = 0$
Разделим все уравнение на 3 для упрощения:
$3x^2 + 7x - 6 = 0$
Решим квадратное уравнение через дискриминант $D = b^2 - 4ac$:
$D = 7^2 - 4 \cdot 3 \cdot (-6) = 49 + 72 = 121 = 11^2$
Найдем корни:
$x_1 = \frac{-b + \sqrt{D}}{2a} = \frac{-7 + 11}{2 \cdot 3} = \frac{4}{6} = \frac{2}{3}$
$x_2 = \frac{-b - \sqrt{D}}{2a} = \frac{-7 - 11}{2 \cdot 3} = \frac{-18}{6} = -3$
Проверим корни по ОДЗ. Корень $x_1 = \frac{2}{3}$ не удовлетворяет условию $x \neq \frac{2}{3}$, поэтому является посторонним. Корень $x_2 = -3$ удовлетворяет ОДЗ.
Ответ: -3
Другие задания:
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