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Номер 132, страница 49 - гдз по алгебре 9 класс учебник Макарычев, Миндюк
Авторы: Макарычев Ю. Н., Миндюк Н. Г., Нешков К. И., Суворова С. Б.
Тип: Учебник
Издательство: Просвещение
Год издания: 2023 - 2026
Уровень обучения: базовый
Цвет обложки: белый, зелёный, фиолетовый
ISBN: 978-5-09-112135-3
Допущено Министерством просвещения Российской Федерации
Популярные ГДЗ в 9 классе
Глава 2. Функции и графики. Параграф 4. Квадратичная функция и её график. 9. Функция у = ах, её график и свойства - номер 132, страница 49.
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" => 171297 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "49" "field_page_end" => null "field_url" => "/9-klass/algebra/makarychev-fgos/132" "field_display_title" => "132" "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 {#1080 #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" => 171105 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Функции и графики" "field_branch_order" => "2" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039 #items: array:1 [ 0 => App\Models\Term {#1038 #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 [ …7] #original: array:7 [ …7] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_page_start" => "33" "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 {#1040 #items: array:1 [ 0 => App\Models\Book {#1041 #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 [ …50] #original: array:50 [ …50] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1077 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 171105 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Функции и графики" "field_branch_order" => "2" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039} "field_page_start" => "33" "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 {#1040} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1077} ] #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 {#1289 #items: array:3 [ 0 => App\Models\Branch {#1078 #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" => 171105 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Функции и графики" "field_branch_order" => "2" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1081 #items: array:1 [ 0 => App\Models\Term {#1079 #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 [ …7] #original: array:7 [ …7] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_page_start" => "33" "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 {#1082 #items: array:1 [ 0 => App\Models\Book {#1083 #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 [ …50] #original: array:50 [ …50] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1119 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 171105 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Функции и графики" "field_branch_order" => "2" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1081} "field_page_start" => "33" "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 {#1082} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1119} ] #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 {#1120 #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" => 171110 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Квадратичная функция и её график" "field_branch_order" => "4" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1121 #items: array:1 [ 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:7 [ …7] #original: array:7 [ …7] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_page_start" => "43" "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 {#1123 #items: array:1 [ 0 => App\Models\Book {#1124 #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 [ …50] #original: array:50 [ …50] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1160 #items: array:1 [ 0 => App\Models\Branch {#1161 #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 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 171110 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Квадратичная функция и её график" "field_branch_order" => "4" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1121} "field_page_start" => "43" "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 {#1123} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1160} ] #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\Branch {#1202 #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" => 171111 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "9. Функция у = ах, её график и свойства" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1203 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "43" "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 {#1204 #items: array:1 [ 0 => App\Models\Book {#1205 #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 [ …50] #original: array:50 [ …50] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1241 #items: array:1 [ 0 => App\Models\Branch {#1242 #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 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 171111 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "9. Функция у = ах, её график и свойства" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1203} "field_page_start" => "43" "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 {#1204} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1241} ] #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 {#1291 #items: array:9 [ 0 => App\Models\Element {#1306 #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" => 178434 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1315 #items: array:1 [ 0 => App\Models\Edition {#1307 #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 [ …21] #original: array:21 [ …21] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "171297" "type" => "task" ] "text" => """ <p><strong>132</strong>. Сократите дробь:</p><figure><figure class="align-center">\n <img src="/media/algebra_09/makarychev-2023/0-00/132.webp?ts=1743930451" alt="Упражнение 132 сократить дробь" loading="lazy" width="836" height="193">\n </figure>\n <figcaption> </figcaption></figure> """ "img" => array:1 [ 0 => array:5 [ "name" => "132-1.jpg" "alt" => null "width" => "1125" "height" => 235 "path" => "/media/algebra_09/makarychev-2023/0-00/132-1.webp?ts=1734090261" ] ] ] #original: array:7 [ "id" => 178434 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1315} "task" => array:2 [ "refs" => "171297" "type" => "task" ] "text" => """ <p><strong>132</strong>. Сократите дробь:</p><figure><figure class="align-center">\n <img src="/media/algebra_09/makarychev-2023/0-00/132.webp?ts=1743930451" alt="Упражнение 132 сократить дробь" loading="lazy" width="836" height="193">\n </figure>\n <figcaption> </figcaption></figure> """ "img" => array:1 [ 0 => array:5 [ "name" => "132-1.jpg" "alt" => null "width" => "1125" "height" => 235 "path" => "/media/algebra_09/makarychev-2023/0-00/132-1.webp?ts=1734090261" ] ] ] #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 {#1313 #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" => 179568 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1323 #items: array:1 [ 0 => App\Models\Edition {#1314 #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 [ …21] #original: array:21 [ …21] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "171297" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "132-1.jpg" "alt" => null "width" => "2092" "height" => 2374 "path" => "/media/algebra_09/makarychev-2023/1-00/132-1.webp?ts=1734090905" ] ] ] #original: array:6 [ "id" => 179568 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1323} "task" => array:2 [ "refs" => "171297" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "132-1.jpg" "alt" => null "width" => "2092" "height" => 2374 "path" => "/media/algebra_09/makarychev-2023/1-00/132-1.webp?ts=1734090905" ] ] ] #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 {#1321 #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" => 180122 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1331 #items: array:1 [ 0 => App\Models\Edition {#1322 #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 [ …21] #original: array:21 [ …21] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "171297" "type" => "task" ] "img" => array:2 [ 0 => array:5 [ "name" => "132-1.png" "alt" => null "width" => "700" "height" => 1882 "path" => "/media/algebra_09/makarychev-2023/2-00/132-1.webp?ts=1734090839" ] 1 => array:5 [ "name" => "132-2.png" "alt" => null "width" => "700" "height" => 2265 "path" => "/media/algebra_09/makarychev-2023/2-00/132-2.webp?ts=1734090839" ] ] ] #original: array:6 [ "id" => 180122 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1331} "task" => array:2 [ "refs" => "171297" "type" => "task" ] "img" => array:2 [ 0 => array:5 [ "name" => "132-1.png" "alt" => null "width" => "700" "height" => 1882 "path" => "/media/algebra_09/makarychev-2023/2-00/132-1.webp?ts=1734090839" ] 1 => array:5 [ "name" => "132-2.png" "alt" => null "width" => "700" "height" => 2265 "path" => "/media/algebra_09/makarychev-2023/2-00/132-2.webp?ts=1734090839" ] ] ] #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\Element {#1329 #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" => 181067 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1339 #items: array:1 [ 0 => App\Models\Edition {#1330 #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 [ …21] #original: array:21 [ …21] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "171297" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "132-1.png" "alt" => null "width" => "650" "height" => 1076 "path" => "/media/algebra_09/makarychev-2023/3-00/132-1.webp?ts=1734091253" ] ] ] #original: array:6 [ "id" => 181067 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1339} "task" => array:2 [ "refs" => "171297" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "132-1.png" "alt" => null "width" => "650" "height" => 1076 "path" => "/media/algebra_09/makarychev-2023/3-00/132-1.webp?ts=1734091253" ] ] ] #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\Element {#1337 #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" => 181738 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1347 #items: array:1 [ 0 => App\Models\Edition {#1338 #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 [ …21] #original: array:21 [ …21] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "171297" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "132-1.png" "alt" => null "width" => "654" "height" => 2156 "path" => "/media/algebra_09/makarychev-2023/4-00/132-1.webp?ts=1734091520" ] ] ] #original: array:6 [ "id" => 181738 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1347} "task" => array:2 [ "refs" => "171297" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "132-1.png" "alt" => null "width" => "654" "height" => 2156 "path" => "/media/algebra_09/makarychev-2023/4-00/132-1.webp?ts=1734091520" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 5 => App\Models\Element {#1345 #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" => 182509 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1355 #items: array:1 [ 0 => App\Models\Edition {#1346 #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 [ …21] #original: array:21 [ …21] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "171297" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "132-1.png" "alt" => null "width" => "718" "height" => 665 "path" => "/media/algebra_09/makarychev-2023/5-00/132-1.webp?ts=1734092353" ] ] ] #original: array:6 [ "id" => 182509 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1355} "task" => array:2 [ "refs" => "171297" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "132-1.png" "alt" => null "width" => "718" "height" => 665 "path" => "/media/algebra_09/makarychev-2023/5-00/132-1.webp?ts=1734092353" ] ] ] #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\Element {#1353 #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" => 183175 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1363 #items: array:1 [ 0 => App\Models\Edition {#1354 #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 [ …21] #original: array:21 [ …21] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "171297" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "132-1.png" "alt" => null "width" => "1368" "height" => 770 "path" => "/media/algebra_09/makarychev-2023/6-00/132-1.webp?ts=1734092551" ] ] ] #original: array:6 [ "id" => 183175 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1363} "task" => array:2 [ "refs" => "171297" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "132-1.png" "alt" => null "width" => "1368" "height" => 770 "path" => "/media/algebra_09/makarychev-2023/6-00/132-1.webp?ts=1734092551" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 7 => App\Models\Element {#1361 #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" => 183654 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1371 #items: array:1 [ 0 => App\Models\Edition {#1362 #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 [ …21] #original: array:21 [ …21] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "171297" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "132-1.jpg" "alt" => null "width" => "1064" "height" => 492 "path" => "/media/algebra_09/makarychev-2023/7-00/132-1.webp?ts=1734093052" ] ] ] #original: array:6 [ "id" => 183654 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1371} "task" => array:2 [ "refs" => "171297" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "132-1.jpg" "alt" => null "width" => "1064" "height" => 492 "path" => "/media/algebra_09/makarychev-2023/7-00/132-1.webp?ts=1734093052" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 8 => App\Models\Element {#1369 #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" => 1348373 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1379 #items: array:1 [ 0 => App\Models\Edition {#1370 #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 [ …21] #original: array:21 [ …21] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "171297" "type" => "task" ] "text" => "<p><strong>а)</strong> Чтобы сократить дробь $\frac{2a - 1}{10a^2 - a - 2}$, необходимо разложить знаменатель на множители. Знаменатель является квадратным трехчленом $10a^2 - a - 2$.</p><p>Для разложения найдем корни соответствующего квадратного уравнения $10a^2 - a - 2 = 0$.</p><p>Вычислим дискриминант по формуле $D = b^2 - 4ac$:</p><p>$D = (-1)^2 - 4 \cdot 10 \cdot (-2) = 1 + 80 = 81 = 9^2$.</p><p>Теперь найдем корни уравнения:</p><p>$a_1 = \frac{-b + \sqrt{D}}{2a} = \frac{1 + 9}{2 \cdot 10} = \frac{10}{20} = \frac{1}{2}$</p><p>$a_2 = \frac{-b - \sqrt{D}}{2a} = \frac{1 - 9}{2 \cdot 10} = \frac{-8}{20} = -\frac{2}{5}$</p><p>Используя формулу разложения квадратного трехчлена $ax^2+bx+c = a(x-x_1)(x-x_2)$, получаем:</p><p>$10a^2 - a - 2 = 10(a - \frac{1}{2})(a - (-\frac{2}{5})) = 10(a - \frac{1}{2})(a + \frac{2}{5})$.</p><p>Для удобства внесем множитель 10 в скобки: $10 = 2 \cdot 5$.</p><p>$10(a - \frac{1}{2})(a + \frac{2}{5}) = (2(a - \frac{1}{2}))(5(a + \frac{2}{5})) = (2a - 1)(5a + 2)$.</p><p>Теперь подставим разложенный знаменатель обратно в дробь:</p><p>$\frac{2a - 1}{(2a - 1)(5a + 2)}$</p><p>Сокращаем общий множитель $(2a - 1)$:</p><p>$\frac{1}{5a + 2}$</p><p>Ответ: $\frac{1}{5a + 2}$</p><p><strong>б)</strong> Чтобы сократить дробь $\frac{6a^2 - 5a + 1}{1 - 4a^2}$, необходимо разложить на множители и числитель, и знаменатель.</p><p>Сначала разложим числитель $6a^2 - 5a + 1$. Найдем корни уравнения $6a^2 - 5a + 1 = 0$.</p><p>Вычислим дискриминант:</p><p>$D = (-5)^2 - 4 \cdot 6 \cdot 1 = 25 - 24 = 1 = 1^2$.</p><p>Найдем корни:</p><p>$a_1 = \frac{5 + 1}{2 \cdot 6} = \frac{6}{12} = \frac{1}{2}$</p><p>$a_2 = \frac{5 - 1}{2 \cdot 6} = \frac{4}{12} = \frac{1}{3}$</p><p>Разложим числитель на множители:</p><p>$6a^2 - 5a + 1 = 6(a - \frac{1}{2})(a - \frac{1}{3}) = (2 \cdot (a - \frac{1}{2}))(3 \cdot (a - \frac{1}{3})) = (2a - 1)(3a - 1)$.</p><p>Теперь разложим знаменатель $1 - 4a^2$. Это разность квадратов $1^2 - (2a)^2$.</p><p>Используем формулу $x^2 - y^2 = (x - y)(x + y)$:</p><p>$1 - 4a^2 = (1 - 2a)(1 + 2a)$.</p><p>Подставим разложенные числитель и знаменатель в дробь:</p><p>$\frac{(2a - 1)(3a - 1)}{(1 - 2a)(1 + 2a)}$</p><p>Заметим, что множители $(2a - 1)$ и $(1 - 2a)$ отличаются только знаком: $2a - 1 = -(1 - 2a)$.</p><p>$\frac{-(1 - 2a)(3a - 1)}{(1 - 2a)(1 + 2a)}$</p><p>Сократим общий множитель $(1 - 2a)$:</p><p>$\frac{-(3a - 1)}{1 + 2a} = \frac{1 - 3a}{1 + 2a}$</p><p>Ответ: $\frac{1 - 3a}{1 + 2a}$</p>" ] #original: array:6 [ "id" => 1348373 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1379} "task" => array:2 [ "refs" => "171297" "type" => "task" ] "text" => "<p><strong>а)</strong> Чтобы сократить дробь $\frac{2a - 1}{10a^2 - a - 2}$, необходимо разложить знаменатель на множители. Знаменатель является квадратным трехчленом $10a^2 - a - 2$.</p><p>Для разложения найдем корни соответствующего квадратного уравнения $10a^2 - a - 2 = 0$.</p><p>Вычислим дискриминант по формуле $D = b^2 - 4ac$:</p><p>$D = (-1)^2 - 4 \cdot 10 \cdot (-2) = 1 + 80 = 81 = 9^2$.</p><p>Теперь найдем корни уравнения:</p><p>$a_1 = \frac{-b + \sqrt{D}}{2a} = \frac{1 + 9}{2 \cdot 10} = \frac{10}{20} = \frac{1}{2}$</p><p>$a_2 = \frac{-b - \sqrt{D}}{2a} = \frac{1 - 9}{2 \cdot 10} = \frac{-8}{20} = -\frac{2}{5}$</p><p>Используя формулу разложения квадратного трехчлена $ax^2+bx+c = a(x-x_1)(x-x_2)$, получаем:</p><p>$10a^2 - a - 2 = 10(a - \frac{1}{2})(a - (-\frac{2}{5})) = 10(a - \frac{1}{2})(a + \frac{2}{5})$.</p><p>Для удобства внесем множитель 10 в скобки: $10 = 2 \cdot 5$.</p><p>$10(a - \frac{1}{2})(a + \frac{2}{5}) = (2(a - \frac{1}{2}))(5(a + \frac{2}{5})) = (2a - 1)(5a + 2)$.</p><p>Теперь подставим разложенный знаменатель обратно в дробь:</p><p>$\frac{2a - 1}{(2a - 1)(5a + 2)}$</p><p>Сокращаем общий множитель $(2a - 1)$:</p><p>$\frac{1}{5a + 2}$</p><p>Ответ: $\frac{1}{5a + 2}$</p><p><strong>б)</strong> Чтобы сократить дробь $\frac{6a^2 - 5a + 1}{1 - 4a^2}$, необходимо разложить на множители и числитель, и знаменатель.</p><p>Сначала разложим числитель $6a^2 - 5a + 1$. Найдем корни уравнения $6a^2 - 5a + 1 = 0$.</p><p>Вычислим дискриминант:</p><p>$D = (-5)^2 - 4 \cdot 6 \cdot 1 = 25 - 24 = 1 = 1^2$.</p><p>Найдем корни:</p><p>$a_1 = \frac{5 + 1}{2 \cdot 6} = \frac{6}{12} = \frac{1}{2}$</p><p>$a_2 = \frac{5 - 1}{2 \cdot 6} = \frac{4}{12} = \frac{1}{3}$</p><p>Разложим числитель на множители:</p><p>$6a^2 - 5a + 1 = 6(a - \frac{1}{2})(a - \frac{1}{3}) = (2 \cdot (a - \frac{1}{2}))(3 \cdot (a - \frac{1}{3})) = (2a - 1)(3a - 1)$.</p><p>Теперь разложим знаменатель $1 - 4a^2$. Это разность квадратов $1^2 - (2a)^2$.</p><p>Используем формулу $x^2 - y^2 = (x - y)(x + y)$:</p><p>$1 - 4a^2 = (1 - 2a)(1 + 2a)$.</p><p>Подставим разложенные числитель и знаменатель в дробь:</p><p>$\frac{(2a - 1)(3a - 1)}{(1 - 2a)(1 + 2a)}$</p><p>Заметим, что множители $(2a - 1)$ и $(1 - 2a)$ отличаются только знаком: $2a - 1 = -(1 - 2a)$.</p><p>$\frac{-(1 - 2a)(3a - 1)}{(1 - 2a)(1 + 2a)}$</p><p>Сократим общий множитель $(1 - 2a)$:</p><p>$\frac{-(3a - 1)}{1 + 2a} = \frac{1 - 3a}{1 + 2a}$</p><p>Ответ: $\frac{1 - 3a}{1 + 2a}$</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" => "171298" "type" => "task" ] "previous" => array:2 [ "refs" => "171296" "type" => "task" ] "book" => 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[] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 1 => App\Models\Term {#1397 #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 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 2 => App\Models\Term {#1398 #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 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => "<!--Текст в низу страницы--> <h2> Учебный процесс с решебником Ключниковой </h2> <p> Изучение алгебры всегда связано с различными недопониманиями. Довольно часто у ребят не хватает времени, чтобы детально проработать каждый параграф. Теорию они проходят в спешке, так как основное внимание сосредоточено в основном на практических заданиях, которые учителя задают на дом в больших количествах. ГДЗ «<strong>Алгебра Учебник Макарычев, Миндюк, Нешков 9 класс (Просвещение, 2023г.)</strong>» позволит школьникам сбалансировать учебный процесс, не упуская ни одной мелочи. </p> <p> Многие ученики испытывают проблемы с пониманием таких аспектов: </p> <ol> <li>Действия над действительными числами.</li> <li>Погрешность и точность приближения?</li> <li>Свойства чётности и нечётности функций.</li> <li>Целое уравнение и его корни.</li> <li>Решение неравенств методом интервалов.</li> <li>Уравнение с двумя переменными и его график.</li> </ol> <p> Современные учебники часто снабжены недостаточно развернутой теорией, что мешает учащимся еще раз пробежаться по материалу, если они пропустили урок или не поняли объяснения преподавателя. Поэтому иногда подростки приступают к решению задач так до конца и не разобравшись в параграфах. Неудивительно, что потом в их работах обнаруживается много ошибок. Благодаря решебнику можно избежать любых недочетов при выполнении номеров. </p> <h2> Почему работать с решебником нужно правильно? </h2> <p> Школьники всегда делятся на две категории. Первые, даже с большим скрипом, но находят решения и ответы самостоятельно, а вот вторые постоянно списывают домашние задания и ничего толком в дисциплине не понимают. Но используя <strong>решебник по алгебре за 9 класс к учебнику Макарычева Ю.Н., Миндюка Н.Г., Нешкова К.И. (Просвещение)</strong> все ребята получают возможность полноценно разобраться в программе этого курса. </p> <p> Неправильное взаимодействие с пособием может привести к следующим последствиям: </p> <ol> <li>материал не будет освоен полностью;</li> <li>постоянные ошибки приведут к снижению успеваемости;</li> <li>отсутствие понимания даже элементарных уравнений;</li> <li>проваленные экзамены.</li> </ol> <p> Соблазн просто списать нужное упражнение несомненно очень велик. Но не стоит забывать о том, что тогда не удастся полностью понять суть изучаемой темы, а это непременно аукнется довольно быстро плохими оценками. Поэтому всегда стоит применять решебник строго по назначению - для самопроверки и работы над ошибками. </p> <h2> Хорошая подготовка д/з с ГДЗ к учебнику Макарычева </h2> <p> Любой учебный процесс - дело непредсказуемое. Даже отличники не застрахованы от получения двоек. Поэтому школьникам не только стоит быть предельно внимательными, но и систематически проверять себя по <strong>готовым решениям к учебнику Макарычева за 9 класс</strong>, написанными в соответствии с ФГОС. Сделать это очень просто, так как пособие находится в онлайн-доступе, и открыть его можно с любого гаджета, подключенного к Интернету. Тренировки со справочником не отнимают много времени, так как авторы снабдили его подробными решениями, верными ответами и многочисленными наглядными примерами, которые легко понять и запомнить. </p> <p> Онлайн-издание пригодится учащимся для многого: </p> <ul> <li>сверки д/з;</li> <li>подготовки к тестированиям;</li> <li>разбора проблематичных параграфов;</li> <li>проработки различных упущений, и т.д.</li> </ul> <p> Некоторые учителя сами советуют своим подопечным использовать решебник, так как прекрасно понимают, что иначе дети просто не справятся с программой. Конечно, есть и еще один вариант - занятия с репетитором. Но в наше время сложно найти преподавателя, который бы смог не только найти общий язык с учеником, но и доступно излагал материал. Кроме того, дополнительные уроки тоже отнимают уйму времени, а именно его у подростков и так мало. Поэтому ГДЗ - лучший вариант быстро освоить предмет и получить качественные навыки. </p>" "breadcrumbs" => array:3 [ "class" => 380 "subject" => 542 "class_subject" => 386 ] ] #original: array:50 [ "id" => 10 "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 {#1290} "field_class" => Illuminate\Database\Eloquent\Collection {#1303} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1301} "field_author" => Illuminate\Database\Eloquent\Collection {#1299} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1292} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1295} "field_country" => Illuminate\Database\Eloquent\Collection {#1377} "field_city" => Illuminate\Database\Eloquent\Collection {#1380} "field_series" => Illuminate\Database\Eloquent\Collection {#1382} "field_umk" => Illuminate\Database\Eloquent\Collection {#1383} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1384} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1386} "field_publication_number" => "16" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1388} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1390} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2023" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => null "field_allowed" => "Допущено Министерством просвещения Российской Федерации" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "934" "field_priority" => "2" "field_default_folder" => "/algebra_09/makarychev-2023/" "field_isbn" => "978-5-09-112135-3" "field_cover" => array:1 [ 0 => "/media/algebra_09/makarychev-2023/covers/cover1.webp?ts=1734038732" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/algebra_09/makarychev-2023/covers/cover1.webp?ts=1734038732" "alt" => "" "width" => "680" "height" => "1065" ] ] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1392} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1393} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1394} "field_url" => "/9-klass/algebra/makarychev-fgos" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1395} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => "<!--Текст в низу страницы--> <h2> Учебный процесс с решебником Ключниковой </h2> <p> Изучение алгебры всегда связано с различными недопониманиями. Довольно часто у ребят не хватает времени, чтобы детально проработать каждый параграф. Теорию они проходят в спешке, так как основное внимание сосредоточено в основном на практических заданиях, которые учителя задают на дом в больших количествах. ГДЗ «<strong>Алгебра Учебник Макарычев, Миндюк, Нешков 9 класс (Просвещение, 2023г.)</strong>» позволит школьникам сбалансировать учебный процесс, не упуская ни одной мелочи. </p> <p> Многие ученики испытывают проблемы с пониманием таких аспектов: </p> <ol> <li>Действия над действительными числами.</li> <li>Погрешность и точность приближения?</li> <li>Свойства чётности и нечётности функций.</li> <li>Целое уравнение и его корни.</li> <li>Решение неравенств методом интервалов.</li> <li>Уравнение с двумя переменными и его график.</li> </ol> <p> Современные учебники часто снабжены недостаточно развернутой теорией, что мешает учащимся еще раз пробежаться по материалу, если они пропустили урок или не поняли объяснения преподавателя. Поэтому иногда подростки приступают к решению задач так до конца и не разобравшись в параграфах. Неудивительно, что потом в их работах обнаруживается много ошибок. Благодаря решебнику можно избежать любых недочетов при выполнении номеров. </p> <h2> Почему работать с решебником нужно правильно? </h2> <p> Школьники всегда делятся на две категории. Первые, даже с большим скрипом, но находят решения и ответы самостоятельно, а вот вторые постоянно списывают домашние задания и ничего толком в дисциплине не понимают. Но используя <strong>решебник по алгебре за 9 класс к учебнику Макарычева Ю.Н., Миндюка Н.Г., Нешкова К.И. 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Поэтому школьникам не только стоит быть предельно внимательными, но и систематически проверять себя по <strong>готовым решениям к учебнику Макарычева за 9 класс</strong>, написанными в соответствии с ФГОС. Сделать это очень просто, так как пособие находится в онлайн-доступе, и открыть его можно с любого гаджета, подключенного к Интернету. Тренировки со справочником не отнимают много времени, так как авторы снабдили его подробными решениями, верными ответами и многочисленными наглядными примерами, которые легко понять и запомнить. </p> <p> Онлайн-издание пригодится учащимся для многого: </p> <ul> <li>сверки д/з;</li> <li>подготовки к тестированиям;</li> <li>разбора проблематичных параграфов;</li> <li>проработки различных упущений, и т.д.</li> </ul> <p> Некоторые учителя сами советуют своим подопечным использовать решебник, так как прекрасно понимают, что иначе дети просто не справятся с программой. Конечно, есть и еще один вариант - занятия с репетитором. Но в наше время сложно найти преподавателя, который бы смог не только найти общий язык с учеником, но и доступно излагал материал. Кроме того, дополнительные уроки тоже отнимают уйму времени, а именно его у подростков и так мало. 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№132 (с. 49)
Условие. №132 (с. 49)
скриншот условия
132. Сократите дробь:
Решение 1. №132 (с. 49)
Решение 2. №132 (с. 49)
Решение 3. №132 (с. 49)
Решение 4. №132 (с. 49)
Решение 5. №132 (с. 49)
Решение 6. №132 (с. 49)
Решение 7. №132 (с. 49)
Решение 8. №132 (с. 49)
а) Чтобы сократить дробь $\frac{2a - 1}{10a^2 - a - 2}$, необходимо разложить знаменатель на множители. Знаменатель является квадратным трехчленом $10a^2 - a - 2$.
Для разложения найдем корни соответствующего квадратного уравнения $10a^2 - a - 2 = 0$.
Вычислим дискриминант по формуле $D = b^2 - 4ac$:
$D = (-1)^2 - 4 \cdot 10 \cdot (-2) = 1 + 80 = 81 = 9^2$.
Теперь найдем корни уравнения:
$a_1 = \frac{-b + \sqrt{D}}{2a} = \frac{1 + 9}{2 \cdot 10} = \frac{10}{20} = \frac{1}{2}$
$a_2 = \frac{-b - \sqrt{D}}{2a} = \frac{1 - 9}{2 \cdot 10} = \frac{-8}{20} = -\frac{2}{5}$
Используя формулу разложения квадратного трехчлена $ax^2+bx+c = a(x-x_1)(x-x_2)$, получаем:
$10a^2 - a - 2 = 10(a - \frac{1}{2})(a - (-\frac{2}{5})) = 10(a - \frac{1}{2})(a + \frac{2}{5})$.
Для удобства внесем множитель 10 в скобки: $10 = 2 \cdot 5$.
$10(a - \frac{1}{2})(a + \frac{2}{5}) = (2(a - \frac{1}{2}))(5(a + \frac{2}{5})) = (2a - 1)(5a + 2)$.
Теперь подставим разложенный знаменатель обратно в дробь:
$\frac{2a - 1}{(2a - 1)(5a + 2)}$
Сокращаем общий множитель $(2a - 1)$:
$\frac{1}{5a + 2}$
Ответ: $\frac{1}{5a + 2}$
б) Чтобы сократить дробь $\frac{6a^2 - 5a + 1}{1 - 4a^2}$, необходимо разложить на множители и числитель, и знаменатель.
Сначала разложим числитель $6a^2 - 5a + 1$. Найдем корни уравнения $6a^2 - 5a + 1 = 0$.
Вычислим дискриминант:
$D = (-5)^2 - 4 \cdot 6 \cdot 1 = 25 - 24 = 1 = 1^2$.
Найдем корни:
$a_1 = \frac{5 + 1}{2 \cdot 6} = \frac{6}{12} = \frac{1}{2}$
$a_2 = \frac{5 - 1}{2 \cdot 6} = \frac{4}{12} = \frac{1}{3}$
Разложим числитель на множители:
$6a^2 - 5a + 1 = 6(a - \frac{1}{2})(a - \frac{1}{3}) = (2 \cdot (a - \frac{1}{2}))(3 \cdot (a - \frac{1}{3})) = (2a - 1)(3a - 1)$.
Теперь разложим знаменатель $1 - 4a^2$. Это разность квадратов $1^2 - (2a)^2$.
Используем формулу $x^2 - y^2 = (x - y)(x + y)$:
$1 - 4a^2 = (1 - 2a)(1 + 2a)$.
Подставим разложенные числитель и знаменатель в дробь:
$\frac{(2a - 1)(3a - 1)}{(1 - 2a)(1 + 2a)}$
Заметим, что множители $(2a - 1)$ и $(1 - 2a)$ отличаются только знаком: $2a - 1 = -(1 - 2a)$.
$\frac{-(1 - 2a)(3a - 1)}{(1 - 2a)(1 + 2a)}$
Сократим общий множитель $(1 - 2a)$:
$\frac{-(3a - 1)}{1 + 2a} = \frac{1 - 3a}{1 + 2a}$
Ответ: $\frac{1 - 3a}{1 + 2a}$
Другие задания:
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