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Номер 252, страница 98 - гдз по алгебре 9 класс учебник Бунимович, Кузнецова
Авторы: Бунимович Е. А., Кузнецова Л. В., Минаева С. С., Рослова Л. О., Суворова С. Б.
Тип: Учебник
Серия: сферы 1-11
Издательство: Просвещение
Год издания: 2018 - 2026
Цвет обложки: оранжевый с диаграммой
ISBN: 978-5-09-051312-8
Популярные ГДЗ в 9 классе
Глава 3. Уравнения и системы уравнений. 3.4 Дробные уравнения - номер 252, страница 98.
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" => 198997 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "98" "field_page_end" => null "field_url" => "/9-klass/algebra/bunimovich-uchebnik/01-252" "field_display_title" => "252" "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 {#1046 #items: array:1 [ 0 => App\Models\Branch {#1045 #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" => 198670 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Уравнения и системы уравнений" "field_branch_order" => "3" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1050 #items: array:1 [ 0 => App\Models\Term {#1047 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "field_short_name" => null ] #original: array:7 [ "id" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "field_short_name" => 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_page_start" => "81" "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 {#1058 #items: array:1 [ 0 => App\Models\Book {#1057 #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" => 2789 "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 {#1062 #items: array:1 [ 0 => App\Models\Term {#1059 #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 [ …6] "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 [ …6] "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 {#1064 #items: array:1 [ 0 => App\Models\Term {#1061 #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 [ …6] "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 [ …6] "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 {#1066 #items: array:1 [ 0 => App\Models\Term {#1063 #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" => 5153 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Просвещение" "field_cases" => null "field_translit" => "prosveschenie" ] #original: array:6 [ "id" => 5153 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Просвещение" "field_cases" => null "field_translit" => "prosveschenie" ] #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 {#1071 #items: array:5 [ 0 => App\Models\Term {#1065 #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" => 3941 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Бунимович" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Евгений" "field_patronymic" => "Абрамович" "field_surname_rp" => null ] #original: array:12 [ "id" => 3941 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Бунимович" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Евгений" "field_patronymic" => "Абрамович" "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 {#1067 #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" => 4848 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Кузнецова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Людмила" "field_patronymic" => "Викторовна" "field_surname_rp" => null ] #original: array:12 [ "id" => 4848 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Кузнецова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Людмила" "field_patronymic" => "Викторовна" "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 {#1060 #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" => 5198 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Минаева" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Светлана" "field_patronymic" => "Станиславовна" "field_surname_rp" => null ] #original: array:12 [ "id" => 5198 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Минаева" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Светлана" "field_patronymic" => "Станиславовна" "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 => "*" ] } 3 => App\Models\Term {#1068 #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" => 5622 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Рослова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Лариса" "field_patronymic" => "Олеговна" "field_surname_rp" => null ] #original: array:12 [ "id" => 5622 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Рослова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Лариса" "field_patronymic" => "Олеговна" "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 => "*" ] } 4 => App\Models\Term {#1069 #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" => 5879 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Суворова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Светлана" "field_patronymic" => "Борисовна" "field_surname_rp" => null ] #original: array:12 [ "id" => 5879 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Суворова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Светлана" "field_patronymic" => "Борисовна" "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 {#1072 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1075 #items: array:1 [ 0 => App\Models\Term {#1070 #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 [ …6] "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 [ …6] "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 {#1077 #items: array:1 [ 0 => App\Models\Term {#1074 #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" => 9 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Россия" "field_cases" => array:6 [ …6] "field_translit" => "rossiya" ] #original: array:6 [ "id" => 9 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Россия" "field_cases" => array:6 [ …6] "field_translit" => "rossiya" ] #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 {#1079 #items: array:1 [ 0 => App\Models\Term {#1076 #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" => 15 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Москва" "field_cases" => array:6 [ …6] "field_translit" => "moskva" ] #original: array:6 [ "id" => 15 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Москва" "field_cases" => array:6 [ …6] "field_translit" => "moskva" ] #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 {#1081 #items: array:1 [ 0 => App\Models\Term {#1078 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:8 [ "id" => 4796 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "сферы 1-11" "field_cases" => null "field_foreign_lang_series" => null "field_transcription_eng" => null "field_translit" => "sfery 1-11" ] #original: array:8 [ "id" => 4796 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "сферы 1-11" "field_cases" => null "field_foreign_lang_series" => null "field_transcription_eng" => null "field_translit" => "sfery 1-11" ] #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_umk" => Illuminate\Database\Eloquent\Collection {#1080 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1073 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1082 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1083 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1084 #items: [] 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{#1085 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1086 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1087 #items: [] #escapeWhenCastingToString: false } "field_url" => "/9-klass/algebra/bunimovich-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1091 #items: array:1 [ 0 => App\Models\Term {#1088 #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" => 50 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "оранжевый" "field_cases" => array:6 [ …6] "field_translit" => "oranzhevyy" ] #original: array:6 [ "id" => 50 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "оранжевый" "field_cases" => 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Алгебраические выражения порой способны поставить в тупик и отличников, что уж говорить о подростках, которые больше склонны к гуманитарным дисциплинам? Поэтому помощь <strong>ГДЗ по алгебре 9 класс учебное пособие Бунимович, Кузнецова, Минаева (Просвещение)</strong> может оказаться незаменимой, особенно при текущих нагрузках. </p> <p> Больше всего трудностей возникает у ребят при изучении следующих тем: </p> <ol> <li>Общие свойства неравенств.</li> <li>Квадратичная функция и её график.</li> <li>Рациональные выражения.</li> <li>Числовые последовательности.</li> <li>Интервальный ряд. Гистограмма.</li> <li>Статистическое оценивание и прогноз.</li> </ol> <p> Уроки нередко проходят срезано, так как за 45 минут преподавателям нужно многое успеть. Они объясняют лишь часть темы, оставляя все остальное для самостоятельного разбора. Но много ли учеников проводит дома свободное время с учебником? Конечно, нет. В основном учащиеся наспех выполняют заданные номера и моментально забывают о них. 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Считается, что чем больше упражнений выполнят школьники, тем лучше они поймут новую тему. Но не всегда такой метод срабатывает. Все же понимание теории - немаловажная составляющая полноценных знаний по предмету. Но в условиях тотальных нагрузок преподавателям просто не остается достаточно времени для проработки всех нюансов. Так что у ребят остается один шанс не упустить ничего важного - это использовать <strong>гдз по алгебре 9 класс к учебнику Бунимович Е.А (2018-2023 гг.)</strong>. </p> <p> Для того чтобы упростить ученикам понимание параграфов, авторы издания разместили в нем: </p> <ul> <li>подробные решения ко всем номерам;</li> <li>верные ответы;</li> <li>готовые графики и заполненные таблицы;</li> <li>детальные наглядные примеры.</li> </ul> <p> Все, что нужно сделать подросткам - это правильно воспользоваться предоставленными сведениями. Расположение решебника и постоянный онлайн-доступ делают работу с ним простым делом, которое займет от силы несколько минут. 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#escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1113 #items: array:3 [ 0 => App\Models\Element {#1106 #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" => 210586 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1098 #items: array:1 [ 0 => App\Models\Edition {#1105 #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" => 700 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1103 …2} "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" => "tolik" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1101 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1102 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1099 …2} "field_content_source" => null ] #original: array:21 [ "id" => 700 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1103 …2} "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" => "tolik" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1101 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1102 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1099 …2} "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" => "198997" "type" => "task" ] "text" => "<p>Решите уравнение (№ 250–253):</p><p><strong>252 a)</strong> $z - \frac{1}{z} = \frac{16}{15}$;</p><p><strong>б)</strong> $x + \frac{1}{x} = -\frac{5}{2}$;</p><p><strong>в)</strong> $2y = 5 - \frac{3}{y}$;</p><p><strong>г)</strong> $\frac{5}{x} + x = 6$;</p><p><strong>д)</strong> $8 - \frac{1}{y} = 7y$;</p><p><strong>е)</strong> $6 = \frac{5}{z} - z$.</p>" "img" => array:2 [ 0 => array:5 [ "name" => "252-1.jpg" "alt" => null "width" => null "height" => null "path" => "/media/algebra_09/bunimovich-u18/0-01/252-1.webp?ts=1734190291" ] 1 => array:5 [ "name" => "252-2.jpg" "alt" => null "width" => null "height" => null "path" => "/media/algebra_09/bunimovich-u18/0-01/252-2.webp?ts=1734190291" ] ] ] #original: array:7 [ "id" => 210586 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1098} "task" => array:2 [ "refs" => "198997" "type" => "task" ] "text" => "<p>Решите уравнение (№ 250–253):</p><p><strong>252 a)</strong> $z - \frac{1}{z} = \frac{16}{15}$;</p><p><strong>б)</strong> $x + \frac{1}{x} = -\frac{5}{2}$;</p><p><strong>в)</strong> $2y = 5 - \frac{3}{y}$;</p><p><strong>г)</strong> $\frac{5}{x} + x = 6$;</p><p><strong>д)</strong> $8 - \frac{1}{y} = 7y$;</p><p><strong>е)</strong> $6 = \frac{5}{z} - z$.</p>" "img" => array:2 [ 0 => array:5 [ "name" => "252-1.jpg" "alt" => null "width" => null "height" => null "path" => "/media/algebra_09/bunimovich-u18/0-01/252-1.webp?ts=1734190291" ] 1 => array:5 [ "name" => "252-2.jpg" "alt" => null "width" => null "height" => null "path" => "/media/algebra_09/bunimovich-u18/0-01/252-2.webp?ts=1734190291" ] ] ] #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 {#1100 #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" => 211733 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1090 #items: array:1 [ 0 => App\Models\Edition {#1097 #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" => 701 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1096 …2} "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" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1094 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1055 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1093 …2} "field_content_source" => null ] #original: array:21 [ "id" => 701 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1096 …2} "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" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1094 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1055 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1093 …2} "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" => "198997" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "252-1.jpg" "alt" => null "width" => null "height" => null "path" => "/media/algebra_09/bunimovich-u18/1-01/252-1.webp?ts=1734190354" ] ] ] #original: array:6 [ "id" => 211733 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1090} "task" => array:2 [ "refs" => "198997" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "252-1.jpg" "alt" => null "width" => null "height" => null "path" => "/media/algebra_09/bunimovich-u18/1-01/252-1.webp?ts=1734190354" ] ] ] #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 {#1092 #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" => 1421510 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1034 #items: array:1 [ 0 => App\Models\Edition {#1089 #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" => 5321 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 2" "field_order" => "3" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1054 …2} "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" => "vadim" "field_edition_type" => "solution" "field_root_dir" => "2-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1052 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1051 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1049 …2} "field_content_source" => null ] #original: array:21 [ "id" => 5321 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 2" "field_order" => "3" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1054 …2} "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" => "vadim" "field_edition_type" => "solution" "field_root_dir" => "2-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1052 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1051 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1049 …2} "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" => "198997" "type" => "task" ] "text" => "<p><strong>а)</strong> $z - \frac{1}{z} = \frac{16}{15}$<br>Данное уравнение является рациональным. Область допустимых значений (ОДЗ) для переменной $z$ определяется условием $z \neq 0$, так как знаменатель не может быть равен нулю.<br>Чтобы избавиться от дробей, умножим обе части уравнения на общий знаменатель, который равен $15z$:<br>$15z \cdot z - 15z \cdot \frac{1}{z} = 15z \cdot \frac{16}{15}$<br>$15z^2 - 15 = 16z$<br>Перенесем все слагаемые в левую часть, чтобы получить стандартное квадратное уравнение вида $az^2 + bz + c = 0$:<br>$15z^2 - 16z - 15 = 0$<br>Решим полученное квадратное уравнение с помощью дискриминанта. Формула дискриминанта: $D = b^2 - 4ac$.<br>$D = (-16)^2 - 4 \cdot 15 \cdot (-15) = 256 + 900 = 1156$<br>Теперь найдем корни уравнения по формуле $z_{1,2} = \frac{-b \pm \sqrt{D}}{2a}$:<br>$\sqrt{D} = \sqrt{1156} = 34$<br>$z_1 = \frac{-(-16) + 34}{2 \cdot 15} = \frac{16 + 34}{30} = \frac{50}{30} = \frac{5}{3}$<br>$z_2 = \frac{-(-16) - 34}{2 \cdot 15} = \frac{16 - 34}{30} = \frac{-18}{30} = -\frac{3}{5}$<br>Оба найденных корня не равны нулю, следовательно, они удовлетворяют ОДЗ.<br>Ответ: $z_1 = \frac{5}{3}; z_2 = -\frac{3}{5}$.</p><p><strong>б)</strong> $x + \frac{1}{x} = -\frac{5}{2}$<br>ОДЗ: $x \neq 0$.<br>Умножим обе части уравнения на общий знаменатель $2x$:<br>$2x \cdot x + 2x \cdot \frac{1}{x} = 2x \cdot (-\frac{5}{2})$<br>$2x^2 + 2 = -5x$<br>Приведем уравнение к стандартному квадратному виду:<br>$2x^2 + 5x + 2 = 0$<br>Найдем дискриминант: $D = b^2 - 4ac = 5^2 - 4 \cdot 2 \cdot 2 = 25 - 16 = 9$.<br>Найдем корни: $\sqrt{D} = 3$.<br>$x_1 = \frac{-5 + 3}{2 \cdot 2} = \frac{-2}{4} = -\frac{1}{2}$<br>$x_2 = \frac{-5 - 3}{2 \cdot 2} = \frac{-8}{4} = -2$<br>Оба корня удовлетворяют ОДЗ.<br>Ответ: $x_1 = -2; x_2 = -\frac{1}{2}$.</p><p><strong>в)</strong> $2y = 5 - \frac{3}{y}$<br>ОДЗ: $y \neq 0$.<br>Умножим обе части уравнения на $y$:<br>$2y \cdot y = 5 \cdot y - \frac{3}{y} \cdot y$<br>$2y^2 = 5y - 3$<br>Приведем уравнение к стандартному квадратному виду:<br>$2y^2 - 5y + 3 = 0$<br>Найдем дискриминант: $D = b^2 - 4ac = (-5)^2 - 4 \cdot 2 \cdot 3 = 25 - 24 = 1$.<br>Найдем корни: $\sqrt{D} = 1$.<br>$y_1 = \frac{-(-5) + 1}{2 \cdot 2} = \frac{5 + 1}{4} = \frac{6}{4} = \frac{3}{2}$<br>$y_2 = \frac{-(-5) - 1}{2 \cdot 2} = \frac{5 - 1}{4} = \frac{4}{4} = 1$<br>Оба корня удовлетворяют ОДЗ.<br>Ответ: $y_1 = 1; y_2 = \frac{3}{2}$.</p><p><strong>г)</strong> $\frac{5}{x} + x = 6$<br>ОДЗ: $x \neq 0$.<br>Умножим обе части уравнения на $x$:<br>$\frac{5}{x} \cdot x + x \cdot x = 6 \cdot x$<br>$5 + x^2 = 6x$<br>Приведем уравнение к стандартному квадратному виду:<br>$x^2 - 6x + 5 = 0$<br>Найдем дискриминант: $D = b^2 - 4ac = (-6)^2 - 4 \cdot 1 \cdot 5 = 36 - 20 = 16$.<br>Найдем корни: $\sqrt{D} = 4$.<br>$x_1 = \frac{-(-6) + 4}{2 \cdot 1} = \frac{6 + 4}{2} = \frac{10}{2} = 5$<br>$x_2 = \frac{-(-6) - 4}{2 \cdot 1} = \frac{6 - 4}{2} = \frac{2}{2} = 1$<br>Оба корня удовлетворяют ОДЗ.<br>Ответ: $x_1 = 1; x_2 = 5$.</p><p><strong>д)</strong> $8 - \frac{1}{y} = 7y$<br>ОДЗ: $y \neq 0$.<br>Умножим обе части уравнения на $y$:<br>$8 \cdot y - \frac{1}{y} \cdot y = 7y \cdot y$<br>$8y - 1 = 7y^2$<br>Приведем уравнение к стандартному квадратному виду:<br>$7y^2 - 8y + 1 = 0$<br>Найдем дискриминант: $D = b^2 - 4ac = (-8)^2 - 4 \cdot 7 \cdot 1 = 64 - 28 = 36$.<br>Найдем корни: $\sqrt{D} = 6$.<br>$y_1 = \frac{-(-8) + 6}{2 \cdot 7} = \frac{8 + 6}{14} = \frac{14}{14} = 1$<br>$y_2 = \frac{-(-8) - 6}{2 \cdot 7} = \frac{8 - 6}{14} = \frac{2}{14} = \frac{1}{7}$<br>Оба корня удовлетворяют ОДЗ.<br>Ответ: $y_1 = \frac{1}{7}; y_2 = 1$.</p><p><strong>е)</strong> $6 = \frac{5}{z} - z$<br>ОДЗ: $z \neq 0$.<br>Умножим обе части уравнения на $z$:<br>$6 \cdot z = \frac{5}{z} \cdot z - z \cdot z$<br>$6z = 5 - z^2$<br>Приведем уравнение к стандартному квадратному виду:<br>$z^2 + 6z - 5 = 0$<br>Найдем дискриминант: $D = b^2 - 4ac = 6^2 - 4 \cdot 1 \cdot (-5) = 36 + 20 = 56$.<br>Найдем корни: $\sqrt{D} = \sqrt{56} = \sqrt{4 \cdot 14} = 2\sqrt{14}$.<br>$z_{1,2} = \frac{-6 \pm 2\sqrt{14}}{2 \cdot 1} = \frac{2(-3 \pm \sqrt{14})}{2} = -3 \pm \sqrt{14}$<br>$z_1 = -3 + \sqrt{14}$<br>$z_2 = -3 - \sqrt{14}$<br>Оба корня удовлетворяют ОДЗ.<br>Ответ: $z_1 = -3 + \sqrt{14}; z_2 = -3 - \sqrt{14}$.</p>" ] #original: array:6 [ "id" => 1421510 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1034} "task" => array:2 [ "refs" => "198997" "type" => "task" ] "text" => "<p><strong>а)</strong> $z - \frac{1}{z} = \frac{16}{15}$<br>Данное уравнение является рациональным. Область допустимых значений (ОДЗ) для переменной $z$ определяется условием $z \neq 0$, так как знаменатель не может быть равен нулю.<br>Чтобы избавиться от дробей, умножим обе части уравнения на общий знаменатель, который равен $15z$:<br>$15z \cdot z - 15z \cdot \frac{1}{z} = 15z \cdot \frac{16}{15}$<br>$15z^2 - 15 = 16z$<br>Перенесем все слагаемые в левую часть, чтобы получить стандартное квадратное уравнение вида $az^2 + bz + c = 0$:<br>$15z^2 - 16z - 15 = 0$<br>Решим полученное квадратное уравнение с помощью дискриминанта. Формула дискриминанта: $D = b^2 - 4ac$.<br>$D = (-16)^2 - 4 \cdot 15 \cdot (-15) = 256 + 900 = 1156$<br>Теперь найдем корни уравнения по формуле $z_{1,2} = \frac{-b \pm \sqrt{D}}{2a}$:<br>$\sqrt{D} = \sqrt{1156} = 34$<br>$z_1 = \frac{-(-16) + 34}{2 \cdot 15} = \frac{16 + 34}{30} = \frac{50}{30} = \frac{5}{3}$<br>$z_2 = \frac{-(-16) - 34}{2 \cdot 15} = \frac{16 - 34}{30} = \frac{-18}{30} = -\frac{3}{5}$<br>Оба найденных корня не равны нулю, следовательно, они удовлетворяют ОДЗ.<br>Ответ: $z_1 = \frac{5}{3}; z_2 = -\frac{3}{5}$.</p><p><strong>б)</strong> $x + \frac{1}{x} = -\frac{5}{2}$<br>ОДЗ: $x \neq 0$.<br>Умножим обе части уравнения на общий знаменатель $2x$:<br>$2x \cdot x + 2x \cdot \frac{1}{x} = 2x \cdot (-\frac{5}{2})$<br>$2x^2 + 2 = -5x$<br>Приведем уравнение к стандартному квадратному виду:<br>$2x^2 + 5x + 2 = 0$<br>Найдем дискриминант: $D = b^2 - 4ac = 5^2 - 4 \cdot 2 \cdot 2 = 25 - 16 = 9$.<br>Найдем корни: $\sqrt{D} = 3$.<br>$x_1 = \frac{-5 + 3}{2 \cdot 2} = \frac{-2}{4} = -\frac{1}{2}$<br>$x_2 = \frac{-5 - 3}{2 \cdot 2} = \frac{-8}{4} = -2$<br>Оба корня удовлетворяют ОДЗ.<br>Ответ: $x_1 = -2; x_2 = -\frac{1}{2}$.</p><p><strong>в)</strong> $2y = 5 - \frac{3}{y}$<br>ОДЗ: $y \neq 0$.<br>Умножим обе части уравнения на $y$:<br>$2y \cdot y = 5 \cdot y - \frac{3}{y} \cdot y$<br>$2y^2 = 5y - 3$<br>Приведем уравнение к стандартному квадратному виду:<br>$2y^2 - 5y + 3 = 0$<br>Найдем дискриминант: $D = b^2 - 4ac = (-5)^2 - 4 \cdot 2 \cdot 3 = 25 - 24 = 1$.<br>Найдем корни: $\sqrt{D} = 1$.<br>$y_1 = \frac{-(-5) + 1}{2 \cdot 2} = \frac{5 + 1}{4} = \frac{6}{4} = \frac{3}{2}$<br>$y_2 = \frac{-(-5) - 1}{2 \cdot 2} = \frac{5 - 1}{4} = \frac{4}{4} = 1$<br>Оба корня удовлетворяют ОДЗ.<br>Ответ: $y_1 = 1; y_2 = \frac{3}{2}$.</p><p><strong>г)</strong> $\frac{5}{x} + x = 6$<br>ОДЗ: $x \neq 0$.<br>Умножим обе части уравнения на $x$:<br>$\frac{5}{x} \cdot x + x \cdot x = 6 \cdot x$<br>$5 + x^2 = 6x$<br>Приведем уравнение к стандартному квадратному виду:<br>$x^2 - 6x + 5 = 0$<br>Найдем дискриминант: $D = b^2 - 4ac = (-6)^2 - 4 \cdot 1 \cdot 5 = 36 - 20 = 16$.<br>Найдем корни: $\sqrt{D} = 4$.<br>$x_1 = \frac{-(-6) + 4}{2 \cdot 1} = \frac{6 + 4}{2} = \frac{10}{2} = 5$<br>$x_2 = \frac{-(-6) - 4}{2 \cdot 1} = \frac{6 - 4}{2} = \frac{2}{2} = 1$<br>Оба корня удовлетворяют ОДЗ.<br>Ответ: $x_1 = 1; x_2 = 5$.</p><p><strong>д)</strong> $8 - \frac{1}{y} = 7y$<br>ОДЗ: $y \neq 0$.<br>Умножим обе части уравнения на $y$:<br>$8 \cdot y - \frac{1}{y} \cdot y = 7y \cdot y$<br>$8y - 1 = 7y^2$<br>Приведем уравнение к стандартному квадратному виду:<br>$7y^2 - 8y + 1 = 0$<br>Найдем дискриминант: $D = b^2 - 4ac = (-8)^2 - 4 \cdot 7 \cdot 1 = 64 - 28 = 36$.<br>Найдем корни: $\sqrt{D} = 6$.<br>$y_1 = \frac{-(-8) + 6}{2 \cdot 7} = \frac{8 + 6}{14} = \frac{14}{14} = 1$<br>$y_2 = \frac{-(-8) - 6}{2 \cdot 7} = \frac{8 - 6}{14} = \frac{2}{14} = \frac{1}{7}$<br>Оба корня удовлетворяют ОДЗ.<br>Ответ: $y_1 = \frac{1}{7}; y_2 = 1$.</p><p><strong>е)</strong> $6 = \frac{5}{z} - z$<br>ОДЗ: $z \neq 0$.<br>Умножим обе части уравнения на $z$:<br>$6 \cdot z = \frac{5}{z} \cdot z - z \cdot z$<br>$6z = 5 - z^2$<br>Приведем уравнение к стандартному квадратному виду:<br>$z^2 + 6z - 5 = 0$<br>Найдем дискриминант: $D = b^2 - 4ac = 6^2 - 4 \cdot 1 \cdot (-5) = 36 + 20 = 56$.<br>Найдем корни: $\sqrt{D} = \sqrt{56} = \sqrt{4 \cdot 14} = 2\sqrt{14}$.<br>$z_{1,2} = \frac{-6 \pm 2\sqrt{14}}{2 \cdot 1} = \frac{2(-3 \pm \sqrt{14})}{2} = -3 \pm \sqrt{14}$<br>$z_1 = -3 + \sqrt{14}$<br>$z_2 = -3 - \sqrt{14}$<br>Оба корня удовлетворяют ОДЗ.<br>Ответ: $z_1 = -3 + \sqrt{14}; z_2 = -3 - \sqrt{14}$.</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" => "198998" "type" => "task" ] "previous" => array:2 [ "refs" => "198996" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1109 #items: array:1 [ 0 => App\Models\Book {#1057} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1112 #items: array:1 [ 0 => App\Models\BookPage {#1042 #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" => 926444 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "98" "field_url" => "/9-klass/algebra/bunimovich-uchebnik/page-98" "field_display_title" => "98" "field_folder" => "1" "field_image_name" => "98" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1040 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1043 #items: array:1 [ 0 => App\Models\Book {#1057} ] #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 {#1041 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1133 #items: array:1 [ 0 => App\Models\Element {#1132 #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" => 1100605 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1134 …2} "book_page" => array:2 [ …2] "img" => array:1 [ …1] ] #original: array:6 [ "id" => 1100605 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1134 …2} "book_page" => array:2 [ …2] "img" => array:1 [ …1] ] #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" => "926445" "type" => "book_page" ] "previous" => array:2 [ "refs" => "926443" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1207 #items: array:12 [ 0 => App\Models\Task {#1225 #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" => 198995 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "98" "field_page_end" => null "field_url" => "/9-klass/algebra/bunimovich-uchebnik/01-250" "field_display_title" => "250" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1226 …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 {#1227 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1228 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1229 …2} "content" => Illuminate\Database\Eloquent\Collection {#1232 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1238 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 198995 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "98" "field_page_end" => null "field_url" => "/9-klass/algebra/bunimovich-uchebnik/01-250" "field_display_title" => "250" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1226 …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 {#1227 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1228 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1229 …2} "content" => Illuminate\Database\Eloquent\Collection {#1232 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1238 …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 {#1231 #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" => 198996 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "98" "field_page_end" => null "field_url" => "/9-klass/algebra/bunimovich-uchebnik/01-251" "field_display_title" => "251" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1230 …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 {#1237 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1239 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1235 …2} "content" => Illuminate\Database\Eloquent\Collection {#1234 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1252 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 198996 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "98" "field_page_end" => null "field_url" => "/9-klass/algebra/bunimovich-uchebnik/01-251" "field_display_title" => "251" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1230 …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 {#1237 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1239 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1235 …2} "content" => Illuminate\Database\Eloquent\Collection {#1234 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1252 …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 => "*" ] } 2 => App\Models\Task {#1236 #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" => 198997 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "98" "field_page_end" => null "field_url" => "/9-klass/algebra/bunimovich-uchebnik/01-252" "field_display_title" => "252" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1233 …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 {#1251 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1253 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1249 …2} "content" => Illuminate\Database\Eloquent\Collection {#1247 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1250 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 198997 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "98" "field_page_end" => null "field_url" => "/9-klass/algebra/bunimovich-uchebnik/01-252" "field_display_title" => "252" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1233 …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 {#1251 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1253 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1249 …2} "content" => Illuminate\Database\Eloquent\Collection {#1247 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1250 …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 => "*" ] } 3 => App\Models\Task {#1248 #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" => 198998 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "98" "field_page_end" => null "field_url" => "/9-klass/algebra/bunimovich-uchebnik/01-253" "field_display_title" => "253" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1261 …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 {#1262 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1263 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1264 …2} "content" => Illuminate\Database\Eloquent\Collection {#1267 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1273 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 198998 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "98" "field_page_end" => null "field_url" => "/9-klass/algebra/bunimovich-uchebnik/01-253" "field_display_title" => "253" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1261 …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 {#1262 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1263 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1264 …2} "content" => Illuminate\Database\Eloquent\Collection {#1267 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1273 …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 => "*" ] } 4 => App\Models\Task {#1266 #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" => 198999 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "98" "field_page_end" => null "field_url" => "/9-klass/algebra/bunimovich-uchebnik/01-254" "field_display_title" => "254" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1265 …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 {#1272 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1274 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1270 …2} "content" => Illuminate\Database\Eloquent\Collection {#1269 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1287 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 198999 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "98" "field_page_end" => null "field_url" => 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#guarded: array:1 [ 0 => "*" ] }
№252 (с. 98)
Условие. №252 (с. 98)
скриншот условия
Решите уравнение (№ 250–253):
252 a) $z - \frac{1}{z} = \frac{16}{15}$;
б) $x + \frac{1}{x} = -\frac{5}{2}$;
в) $2y = 5 - \frac{3}{y}$;
г) $\frac{5}{x} + x = 6$;
д) $8 - \frac{1}{y} = 7y$;
е) $6 = \frac{5}{z} - z$.
Решение. №252 (с. 98)
Решение 2. №252 (с. 98)
а) $z - \frac{1}{z} = \frac{16}{15}$
Данное уравнение является рациональным. Область допустимых значений (ОДЗ) для переменной $z$ определяется условием $z \neq 0$, так как знаменатель не может быть равен нулю.
Чтобы избавиться от дробей, умножим обе части уравнения на общий знаменатель, который равен $15z$:
$15z \cdot z - 15z \cdot \frac{1}{z} = 15z \cdot \frac{16}{15}$
$15z^2 - 15 = 16z$
Перенесем все слагаемые в левую часть, чтобы получить стандартное квадратное уравнение вида $az^2 + bz + c = 0$:
$15z^2 - 16z - 15 = 0$
Решим полученное квадратное уравнение с помощью дискриминанта. Формула дискриминанта: $D = b^2 - 4ac$.
$D = (-16)^2 - 4 \cdot 15 \cdot (-15) = 256 + 900 = 1156$
Теперь найдем корни уравнения по формуле $z_{1,2} = \frac{-b \pm \sqrt{D}}{2a}$:
$\sqrt{D} = \sqrt{1156} = 34$
$z_1 = \frac{-(-16) + 34}{2 \cdot 15} = \frac{16 + 34}{30} = \frac{50}{30} = \frac{5}{3}$
$z_2 = \frac{-(-16) - 34}{2 \cdot 15} = \frac{16 - 34}{30} = \frac{-18}{30} = -\frac{3}{5}$
Оба найденных корня не равны нулю, следовательно, они удовлетворяют ОДЗ.
Ответ: $z_1 = \frac{5}{3}; z_2 = -\frac{3}{5}$.
б) $x + \frac{1}{x} = -\frac{5}{2}$
ОДЗ: $x \neq 0$.
Умножим обе части уравнения на общий знаменатель $2x$:
$2x \cdot x + 2x \cdot \frac{1}{x} = 2x \cdot (-\frac{5}{2})$
$2x^2 + 2 = -5x$
Приведем уравнение к стандартному квадратному виду:
$2x^2 + 5x + 2 = 0$
Найдем дискриминант: $D = b^2 - 4ac = 5^2 - 4 \cdot 2 \cdot 2 = 25 - 16 = 9$.
Найдем корни: $\sqrt{D} = 3$.
$x_1 = \frac{-5 + 3}{2 \cdot 2} = \frac{-2}{4} = -\frac{1}{2}$
$x_2 = \frac{-5 - 3}{2 \cdot 2} = \frac{-8}{4} = -2$
Оба корня удовлетворяют ОДЗ.
Ответ: $x_1 = -2; x_2 = -\frac{1}{2}$.
в) $2y = 5 - \frac{3}{y}$
ОДЗ: $y \neq 0$.
Умножим обе части уравнения на $y$:
$2y \cdot y = 5 \cdot y - \frac{3}{y} \cdot y$
$2y^2 = 5y - 3$
Приведем уравнение к стандартному квадратному виду:
$2y^2 - 5y + 3 = 0$
Найдем дискриминант: $D = b^2 - 4ac = (-5)^2 - 4 \cdot 2 \cdot 3 = 25 - 24 = 1$.
Найдем корни: $\sqrt{D} = 1$.
$y_1 = \frac{-(-5) + 1}{2 \cdot 2} = \frac{5 + 1}{4} = \frac{6}{4} = \frac{3}{2}$
$y_2 = \frac{-(-5) - 1}{2 \cdot 2} = \frac{5 - 1}{4} = \frac{4}{4} = 1$
Оба корня удовлетворяют ОДЗ.
Ответ: $y_1 = 1; y_2 = \frac{3}{2}$.
г) $\frac{5}{x} + x = 6$
ОДЗ: $x \neq 0$.
Умножим обе части уравнения на $x$:
$\frac{5}{x} \cdot x + x \cdot x = 6 \cdot x$
$5 + x^2 = 6x$
Приведем уравнение к стандартному квадратному виду:
$x^2 - 6x + 5 = 0$
Найдем дискриминант: $D = b^2 - 4ac = (-6)^2 - 4 \cdot 1 \cdot 5 = 36 - 20 = 16$.
Найдем корни: $\sqrt{D} = 4$.
$x_1 = \frac{-(-6) + 4}{2 \cdot 1} = \frac{6 + 4}{2} = \frac{10}{2} = 5$
$x_2 = \frac{-(-6) - 4}{2 \cdot 1} = \frac{6 - 4}{2} = \frac{2}{2} = 1$
Оба корня удовлетворяют ОДЗ.
Ответ: $x_1 = 1; x_2 = 5$.
д) $8 - \frac{1}{y} = 7y$
ОДЗ: $y \neq 0$.
Умножим обе части уравнения на $y$:
$8 \cdot y - \frac{1}{y} \cdot y = 7y \cdot y$
$8y - 1 = 7y^2$
Приведем уравнение к стандартному квадратному виду:
$7y^2 - 8y + 1 = 0$
Найдем дискриминант: $D = b^2 - 4ac = (-8)^2 - 4 \cdot 7 \cdot 1 = 64 - 28 = 36$.
Найдем корни: $\sqrt{D} = 6$.
$y_1 = \frac{-(-8) + 6}{2 \cdot 7} = \frac{8 + 6}{14} = \frac{14}{14} = 1$
$y_2 = \frac{-(-8) - 6}{2 \cdot 7} = \frac{8 - 6}{14} = \frac{2}{14} = \frac{1}{7}$
Оба корня удовлетворяют ОДЗ.
Ответ: $y_1 = \frac{1}{7}; y_2 = 1$.
е) $6 = \frac{5}{z} - z$
ОДЗ: $z \neq 0$.
Умножим обе части уравнения на $z$:
$6 \cdot z = \frac{5}{z} \cdot z - z \cdot z$
$6z = 5 - z^2$
Приведем уравнение к стандартному квадратному виду:
$z^2 + 6z - 5 = 0$
Найдем дискриминант: $D = b^2 - 4ac = 6^2 - 4 \cdot 1 \cdot (-5) = 36 + 20 = 56$.
Найдем корни: $\sqrt{D} = \sqrt{56} = \sqrt{4 \cdot 14} = 2\sqrt{14}$.
$z_{1,2} = \frac{-6 \pm 2\sqrt{14}}{2 \cdot 1} = \frac{2(-3 \pm \sqrt{14})}{2} = -3 \pm \sqrt{14}$
$z_1 = -3 + \sqrt{14}$
$z_2 = -3 - \sqrt{14}$
Оба корня удовлетворяют ОДЗ.
Ответ: $z_1 = -3 + \sqrt{14}; z_2 = -3 - \sqrt{14}$.
Другие задания:
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