Номер 332, страница 82, часть 1 - гдз по математике 5 класс учебник Петерсон, Дорофеев

Математика, 5 класс Учебник, авторы: Петерсон Людмила Георгиевна, Дорофеев Георгий Владимирович, издательство Просвещение, Москва

Авторы: Петерсон Л. Г., Дорофеев Г. В.

Тип: Учебник

Издательство: Просвещение

Часть: 1

ISBN: 978-5-09-107330-0

Часть 1. Глава 1. Математический язык. Параграф 3. Язык и логика. 5. Введение обозначений - номер 332, страница 82.

App\Models\Task {#1030 // resources/views/models/task/default.blade.php
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  #table: "tasks"
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          #connection: "mysql"
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                          #attributes: array:10 [
                            "id" => 6484
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
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                              "field_genitive_case" => "математики"
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                            "field_foreign_lang_name" => null
                            "field_short_name" => null
                            "field_subject_type" => "technical_subject"
                            "field_translit" => "matematika"
                          ]
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                            "id" => 6484
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
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                            "field_cases" => array:6 [
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                              "field_genitive_case" => "математики"
                              "field_nominative_case" => "математика"
                               …1
                            ]
                            "field_foreign_lang_name" => null
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                            "field_subject_type" => "technical_subject"
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                        0 => App\Models\Term {#1189
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
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                          #attributes: array:6 [
                            "id" => 5445
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "5"
                            "field_cases" => array:6 [ …6]
                            "field_translit" => "pjatyj"
                          ]
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                            "id" => 5445
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "5"
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                            "field_translit" => "pjatyj"
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                    "field_publisher" => Illuminate\Database\Eloquent\Collection {#1190
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                        0 => App\Models\Term {#1191
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
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                          #with: []
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                          #attributes: array:6 [
                            "id" => 5153
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Просвещение"
                            "field_cases" => null
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                          ]
                          #original: array:6 [
                            "id" => 5153
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Просвещение"
                            "field_cases" => null
                            "field_translit" => "prosveschenie"
                          ]
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                          #dateFormat: null
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                          #dispatchesEvents: []
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                          #relations: []
                          #touches: []
                          +timestamps: true
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                          #hidden: []
                          #visible: []
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                            0 => "*"
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                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_author" => Illuminate\Database\Eloquent\Collection {#1192
                      #items: array:2 [
                        0 => App\Models\Term {#1193
                          #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" => 5448
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Петерсон"
                            "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" => "Георгиевна"
                            "field_surname_rp" => null
                          ]
                          #original: array:12 [
                            "id" => 5448
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Петерсон"
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                            "field_degree_rp" => null
                            "field_foreign_lang_name" => null
                            "field_foreign_lang_patronymic" => null
                            "field_foreign_lang_surname" => null
                            "field_name" => "Людмила"
                            "field_patronymic" => "Георгиевна"
                            "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 {#1194
                          #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" => 4283
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Дорофеев"
                            "field_bio" => null
                            "field_degree_rp" => null
                            "field_foreign_lang_name" => null
                            "field_foreign_lang_patronymic" => null
                            "field_foreign_lang_surname" => null
                            "field_name" => "Георгий"
                            "field_patronymic" => "Владимирович"
                            "field_surname_rp" => null
                          ]
                          #original: array:12 [
                            "id" => 4283
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Дорофеев"
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                            "field_foreign_lang_patronymic" => null
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                            "field_patronymic" => "Владимирович"
                            "field_surname_rp" => null
                          ]
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                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
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                          #touches: []
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                            0 => "*"
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                      ]
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                    }
                    "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1195
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_book_type" => Illuminate\Database\Eloquent\Collection {#1196
                      #items: array:1 [
                        0 => App\Models\Term {#1197
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
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                          #perPage: 15
                          +exists: true
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                          #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
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                          #dateFormat: null
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                          #hidden: []
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                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_country" => Illuminate\Database\Eloquent\Collection {#1198
                      #items: array:1 [
                        0 => App\Models\Term {#1199
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
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                          #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"
                          ]
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                            "id" => 9
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Россия"
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                            "field_translit" => "rossiya"
                          ]
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                      ]
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                    "field_city" => Illuminate\Database\Eloquent\Collection {#1200
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                        0 => App\Models\Term {#1201
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
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                          #withCount: []
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                          #perPage: 15
                          +exists: true
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                          #escapeWhenCastingToString: false
                          #attributes: array:6 [
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                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Москва"
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                            "field_translit" => "moskva"
                          ]
                          #original: array:6 [
                            "id" => 15
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Москва"
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                            "field_translit" => "moskva"
                          ]
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                          #dateFormat: null
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                      ]
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                    "field_series" => Illuminate\Database\Eloquent\Collection {#1202
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_umk" => Illuminate\Database\Eloquent\Collection {#1203
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1204
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1205
                      #items: array:1 [
                        0 => App\Models\Term {#1206
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
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                          #withCount: []
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                          #attributes: array:10 [
                            "id" => 25
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "ФГОС (новый)"
                            "field_cases" => array:6 [ …6]
                            "field_color" => "красный"
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                          ]
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                            "updated_at" => null
                            "name" => "ФГОС (новый)"
                            "field_cases" => array:6 [ …6]
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                          ]
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                      ]
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                    "field_publication_number" => null
                    "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1207
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                      #escapeWhenCastingToString: false
                    }
                    "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1208
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_under_the_edition_degree" => null
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                    "field_part" => "1, 2"
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                    "field_default_folder" => "/matematika_05/peterson-u/"
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                    "field_cover" => array:2 [
                      0 => "/media/matematika_05/peterson-u/covers/cover1.webp?ts=1773224118"
                      1 => "/media/matematika_05/peterson-u/covers/cover2.webp?ts=1773224118"
                    ]
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                      0 => ""
                      1 => ""
                    ]
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                    ]
                    "field_popular_book" => "0"
                    "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1209
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_new_book" => Illuminate\Database\Eloquent\Collection {#1210
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_old_book" => Illuminate\Database\Eloquent\Collection {#1211
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_url" => "/5-klass/matematika/peterson-uchebnik"
                    "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1212
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_metatags_title" => null
                    "field_metatags_description" => null
                    "field_h1" => null
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                    "field_description_bottom" => null
                    "breadcrumbs" => array:3 [
                      "class" => 376
                      "subject" => 544
                      "class_subject" => 398
                    ]
                  ]
                  #original: array:50 [
                    "id" => 62
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "field_tree_default_status" => "tasks"
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                    "field_subject" => Illuminate\Database\Eloquent\Collection {#1187}
                    "field_class" => Illuminate\Database\Eloquent\Collection {#1188}
                    "field_publisher" => Illuminate\Database\Eloquent\Collection {#1190}
                    "field_author" => Illuminate\Database\Eloquent\Collection {#1192}
                    "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1195}
                    "field_book_type" => Illuminate\Database\Eloquent\Collection {#1196}
                    "field_country" => Illuminate\Database\Eloquent\Collection {#1198}
                    "field_city" => Illuminate\Database\Eloquent\Collection {#1200}
                    "field_series" => Illuminate\Database\Eloquent\Collection {#1202}
                    "field_umk" => Illuminate\Database\Eloquent\Collection {#1203}
                    "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1204}
                    "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1205}
                    "field_publication_number" => null
                    "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1207}
                    "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1208}
                    "field_under_the_edition_degree" => null
                    "field_cover_description" => null
                    "field_publication_year" => null
                    "field_publication_year_until" => null
                    "field_part" => "1, 2"
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                    "field_second_foreign_language" => null
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                    "field_link_to_source" => null
                    "field_tasks_count" => "2021"
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                    "field_default_folder" => "/matematika_05/peterson-u/"
                    "field_isbn" => "978-5-09-107330-0"
                    "field_cover" => array:2 [
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                      1 => "/media/matematika_05/peterson-u/covers/cover2.webp?ts=1773224118"
                    ]
                    "field_cover_alts" => array:2 [
                      0 => ""
                      1 => ""
                    ]
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                      ]
                      1 => array:4 [
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                    "field_popular_book" => "0"
                    "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1209}
                    "field_new_book" => Illuminate\Database\Eloquent\Collection {#1210}
                    "field_old_book" => Illuminate\Database\Eloquent\Collection {#1211}
                    "field_url" => "/5-klass/matematika/peterson-uchebnik"
                    "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1212}
                    "field_metatags_title" => null
                    "field_metatags_description" => null
                    "field_h1" => null
                    "field_description_top" => null
                    "field_description_bottom" => null
                    "breadcrumbs" => array:3 [
                      "class" => 376
                      "subject" => 544
                      "class_subject" => 398
                    ]
                  ]
                  #changes: []
                  #casts: []
                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
                  #observables: []
                  #relations: []
                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
              ]
              #escapeWhenCastingToString: false
            }
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1213
              #items: []
              #escapeWhenCastingToString: false
            }
          ]
          #original: array:24 [
            "id" => 2157448
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => null
            "field_branch_order" => "1"
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1186}
            "field_page_start" => "3"
            "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" => array:1 [
              0 => "/media/matematika_05/peterson-u/covers/cover1.webp?ts=1773224118"
            ]
            "field_branch_covers" => array:1 [
              0 => array:4 [
                "path" => "/media/matematika_05/peterson-u/covers/cover1.webp?ts=1773224118"
                "alt" => ""
                "width" => "2306"
                "height" => "3004"
              ]
            ]
            "book" => Illuminate\Database\Eloquent\Collection {#1215}
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1213}
          ]
          #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 {#1214
          #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" => 2157449
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => "Математический язык"
            "field_branch_order" => "1"
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1219
              #items: array:1 [
                0 => App\Models\Term {#1216
                  #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 [
                      "field_accusative_case" => "Главу"
                      "field_creative_case" => "Главой"
                      "field_dative_case" => "Главе"
                      "field_genitive_case" => "Главы"
                      "field_nominative_case" => "Глава"
                      "field_prepositional_case" => "Главе"
                    ]
                    "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 [
                      "field_accusative_case" => "Главу"
                      "field_creative_case" => "Главой"
                      "field_dative_case" => "Главе"
                      "field_genitive_case" => "Главы"
                      "field_nominative_case" => "Глава"
                      "field_prepositional_case" => "Главе"
                    ]
                    "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" => "3"
            "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 {#1218
              #items: array:1 [
                0 => App\Models\Book {#1185}
              ]
              #escapeWhenCastingToString: false
            }
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1217
              #items: array:1 [
                0 => App\Models\Branch {#1034}
              ]
              #escapeWhenCastingToString: false
            }
          ]
          #original: array:24 [
            "id" => 2157449
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => "Математический язык"
            "field_branch_order" => "1"
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1219}
            "field_page_start" => "3"
            "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 {#1218}
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1217}
          ]
          #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 {#1220
          #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" => 2157458
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => "Язык и логика"
            "field_branch_order" => "3"
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1224
              #items: array:1 [
                0 => App\Models\Term {#1221
                  #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" => 32
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "Параграф"
                    "field_cases" => array:6 [
                      "field_accusative_case" => "Параграф"
                      "field_creative_case" => "Параграфом"
                      "field_dative_case" => "Параграфу"
                      "field_genitive_case" => "Параграфа"
                      "field_nominative_case" => "Параграф"
                      "field_prepositional_case" => "Параграфе"
                    ]
                    "field_page_check_not_needed" => null
                    "field_short_name" => "§"
                  ]
                  #original: array:7 [
                    "id" => 32
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "Параграф"
                    "field_cases" => array:6 [
                      "field_accusative_case" => "Параграф"
                      "field_creative_case" => "Параграфом"
                      "field_dative_case" => "Параграфу"
                      "field_genitive_case" => "Параграфа"
                      "field_nominative_case" => "Параграф"
                      "field_prepositional_case" => "Параграфе"
                    ]
                    "field_page_check_not_needed" => null
                    "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_page_start" => "55"
            "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 {#1223
              #items: array:1 [
                0 => App\Models\Book {#1185}
              ]
              #escapeWhenCastingToString: false
            }
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1292
              #items: array:1 [
                0 => App\Models\Branch {#1222
                  #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" => 2157449
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "field_display_title" => "Математический язык"
                    "field_branch_order" => "1"
                    "field_url" => null
                    "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1226
                      #items: array:1 [ …1]
                      #escapeWhenCastingToString: false
                    }
                    "field_page_start" => "3"
                    "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 {#1227
                      #items: array:1 [ …1]
                      #escapeWhenCastingToString: false
                    }
                    "branch_parent" => Illuminate\Database\Eloquent\Collection {#1256
                      #items: array:1 [ …1]
                      #escapeWhenCastingToString: false
                    }
                  ]
                  #original: array:24 [
                    "id" => 2157449
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "field_display_title" => "Математический язык"
                    "field_branch_order" => "1"
                    "field_url" => null
                    "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1226}
                    "field_page_start" => "3"
                    "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 {#1227}
                    "branch_parent" => Illuminate\Database\Eloquent\Collection {#1256}
                  ]
                  #changes: []
                  #casts: []
                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
                  #observables: []
                  #relations: []
                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
              ]
              #escapeWhenCastingToString: false
            }
          ]
          #original: array:24 [
            "id" => 2157458
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => "Язык и логика"
            "field_branch_order" => "3"
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1224}
            "field_page_start" => "55"
            "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 {#1223}
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1292}
          ]
          #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\Branch {#1290
          #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" => 2157463
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => "5. Введение обозначений"
            "field_branch_order" => null
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1291
              #items: []
              #escapeWhenCastingToString: false
            }
            "field_page_start" => "74"
            "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 {#1293
              #items: array:1 [
                0 => App\Models\Book {#1185}
              ]
              #escapeWhenCastingToString: false
            }
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1302
              #items: array:1 [
                0 => App\Models\Branch {#1301
                  #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" => 2157458
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "field_display_title" => "Язык и логика"
                    "field_branch_order" => "3"
                    "field_url" => null
                    "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1303
                      #items: array:1 [ …1]
                      #escapeWhenCastingToString: false
                    }
                    "field_page_start" => "55"
                    "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 {#1304
                      #items: array:1 [ …1]
                      #escapeWhenCastingToString: false
                    }
                    "branch_parent" => Illuminate\Database\Eloquent\Collection {#1305
                      #items: array:1 [ …1]
                      #escapeWhenCastingToString: false
                    }
                  ]
                  #original: array:24 [
                    "id" => 2157458
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "field_display_title" => "Язык и логика"
                    "field_branch_order" => "3"
                    "field_url" => null
                    "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1303}
                    "field_page_start" => "55"
                    "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 {#1304}
                    "branch_parent" => Illuminate\Database\Eloquent\Collection {#1305}
                  ]
                  #changes: []
                  #casts: []
                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
                  #observables: []
                  #relations: []
                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
              ]
              #escapeWhenCastingToString: false
            }
          ]
          #original: array:24 [
            "id" => 2157463
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => "5. Введение обозначений"
            "field_branch_order" => null
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1291}
            "field_page_start" => "74"
            "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 {#1293}
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1302}
          ]
          #changes: []
          #casts: []
          #classCastCache: []
          #attributeCastCache: []
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            0 => "*"
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      ]
      #escapeWhenCastingToString: false
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    "content" => Illuminate\Database\Eloquent\Collection {#1104
      #items: array:2 [
        0 => App\Models\Element {#1165
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                0 => App\Models\Edition {#1164
                  #connection: "mysql"
                  #table: "editions"
                  #primaryKey: "id"
                  #keyType: "int"
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                    "id" => 9500
                    "created_at" => "2026-04-10 13:58:26"
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                    "field_content_type" => "free"
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                    "field_solution_author" => "Автор"
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                    "field_edition_type" => "statement"
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                    "id" => 9500
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "title" => "Условие"
                    "field_order" => "1"
                    "field_publisher" => Illuminate\Database\Eloquent\Collection {#1161}
                    "field_content_type" => "free"
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                    "field_solution_author" => "Автор"
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                    "field_comment" => null
                    "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1160}
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                    "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1159}
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                  ]
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                    0 => "*"
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                }
              ]
              #escapeWhenCastingToString: false
            }
            "task" => array:2 [
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              "type" => "task"
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            "img" => array:1 [
              0 => array:5 [
                "name" => "332-1.jpg"
                "alt" => null
                "width" => "1892"
                "height" => 257
                "path" => "/media/matematika_05/peterson-u/0-11/332-1.webp?ts=1773225381"
              ]
            ]
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            "id" => 2019611
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "edition" => Illuminate\Database\Eloquent\Collection {#1157}
            "task" => array:2 [
              "refs" => "2157841"
              "type" => "task"
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            "img" => array:1 [
              0 => array:5 [
                "name" => "332-1.jpg"
                "alt" => null
                "width" => "1892"
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              ]
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            0 => "*"
          ]
        }
        1 => App\Models\Element {#1158
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          #table: "elements"
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          #keyType: "int"
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          #attributes: array:6 [
            "id" => 2020239
            "created_at" => "2026-04-10 13:58:26"
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            "edition" => Illuminate\Database\Eloquent\Collection {#1149
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                0 => App\Models\Edition {#1156
                  #connection: "mysql"
                  #table: "editions"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: false
                  #with: []
                  #withCount: []
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                  #escapeWhenCastingToString: false
                  #attributes: array:21 [
                    "id" => 9501
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "title" => "Решение"
                    "field_order" => "2"
                    "field_publisher" => Illuminate\Database\Eloquent\Collection {#1155
                      #items: array:1 [ …1]
                      #escapeWhenCastingToString: false
                    }
                    "field_content_type" => "free"
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                    "field_page_content_mode" => ""
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                    "field_page_content_text_checked" => "0"
                    "field_solution_author" => "Неизвестный"
                    "field_moderator" => "pasha"
                    "field_edition_type" => "solution"
                    "field_root_dir" => "1-"
                    "field_responsible" => Illuminate\Database\Eloquent\Collection {#1152
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_comment" => null
                    "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1153
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                      #escapeWhenCastingToString: false
                    }
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                  ]
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                    "title" => "Решение"
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                    "field_publisher" => Illuminate\Database\Eloquent\Collection {#1155}
                    "field_content_type" => "free"
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                    "field_page_content_text_checked" => "0"
                    "field_solution_author" => "Неизвестный"
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                    "field_edition_type" => "solution"
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                    "field_responsible" => Illuminate\Database\Eloquent\Collection {#1152}
                    "field_comment" => null
                    "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1153}
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                    "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1151}
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                  ]
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                    0 => "*"
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                }
              ]
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            }
            "task" => array:2 [
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              "type" => "task"
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            "img" => array:1 [
              0 => array:5 [
                "name" => "332-1.jpg"
                "alt" => null
                "width" => "1372"
                "height" => 644
                "path" => "/media/matematika_05/peterson-u/1-11/332-1.webp?ts=1773225403"
              ]
            ]
          ]
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            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "edition" => Illuminate\Database\Eloquent\Collection {#1149}
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              "refs" => "2157841"
              "type" => "task"
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    "book" => Illuminate\Database\Eloquent\Collection {#1168
      #items: array:1 [
        0 => App\Models\Book {#1185}
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      #escapeWhenCastingToString: false
    }
    "page" => Illuminate\Database\Eloquent\Collection {#1169
      #items: array:1 [
        0 => App\Models\BookPage {#1141
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          #table: "book_pages"
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          #attributes: array:21 [
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            "created_at" => "2026-04-10 13:58:26"
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            "field_display_title" => "82"
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                0 => App\Models\Branch {#1148
                  #connection: "mysql"
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                    "field_branch_order" => "2"
                    "field_url" => null
                    "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1146 …2}
                    "field_page_start" => "4"
                    "field_branch_display" => "0"
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                    "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
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                    "field_branch_cover" => array:1 [ …1]
                    "field_branch_covers" => array:1 [ …1]
                    "book" => Illuminate\Database\Eloquent\Collection {#1147 …2}
                    "branch_parent" => Illuminate\Database\Eloquent\Collection {#1116 …2}
                  ]
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                    "id" => 2157483
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
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                    "field_branch_order" => "2"
                    "field_url" => null
                    "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1146 …2}
                    "field_page_start" => "4"
                    "field_branch_display" => "0"
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                    "field_display_branch_in_title" => "1"
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                    "field_display_branch_page" => "1"
                    "field_branch_title_in_content" => "0"
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                    "field_h1" => null
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                    "field_branch_cover" => array:1 [ …1]
                    "field_branch_covers" => array:1 [ …1]
                    "book" => Illuminate\Database\Eloquent\Collection {#1147 …2}
                    "branch_parent" => Illuminate\Database\Eloquent\Collection {#1116 …2}
                  ]
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                    0 => "*"
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                }
              ]
              #escapeWhenCastingToString: false
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            "field_weight" => "0"
            "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1113
              #items: array:1 [
                0 => App\Models\Book {#1185}
              ]
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            "field_metatags_description" => null
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            "edition_groups" => Illuminate\Database\Eloquent\Collection {#1114
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              #escapeWhenCastingToString: false
            }
            "content" => Illuminate\Database\Eloquent\Collection {#1102
              #items: array:1 [
                0 => App\Models\Element {#1075
                  #connection: "mysql"
                  #table: "elements"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: true
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                  #withCount: []
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                  #attributes: array:6 [
                    "id" => 2023543
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "edition" => Illuminate\Database\Eloquent\Collection {#1101 …2}
                    "book_page" => array:2 [ …2]
                    "img" => array:1 [ …1]
                  ]
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                    "id" => 2023543
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                    "updated_at" => null
                    "edition" => Illuminate\Database\Eloquent\Collection {#1101 …2}
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                    0 => "*"
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                }
              ]
              #escapeWhenCastingToString: false
            }
            "next" => array:2 [
              "refs" => "2161819"
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            "previous" => array:2 [
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            "tasks" => Illuminate\Database\Eloquent\Collection {#1110
              #items: array:2 [
                0 => App\Models\Task {#1097
                  #connection: "mysql"
                  #table: "tasks"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: true
                  #with: []
                  #withCount: []
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                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:24 [
                    "id" => 2158764
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "field_page_start" => "82"
                    "field_page_end" => null
                    "field_url" => "/5-klass/matematika/peterson-uchebnik/22-401"
                    "field_display_title" => "401"
                    "field_outside_task" => null
                    "field_task_type" => Illuminate\Database\Eloquent\Collection {#1095 …2}
                    "field_metatags_title" => null
                    "field_metatags_description" => null
                    "field_h1" => null
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                    "field_description_bottom" => null
                    "field_match" => null
                    "breadcrumbs" => []
                    "edition_groups" => Illuminate\Database\Eloquent\Collection {#1096 …2}
                    "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1094 …2}
                    "parent_branches" => Illuminate\Database\Eloquent\Collection {#1443 …2}
                    "content" => Illuminate\Database\Eloquent\Collection {#1370 …2}
                    "next" => array:2 [ …2]
                    "previous" => array:2 [ …2]
                    "book" => Illuminate\Database\Eloquent\Collection {#1439 …2}
                    "page" => array:2 [ …2]
                  ]
                  #original: array:24 [
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                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "field_page_start" => "82"
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                    "field_url" => "/5-klass/matematika/peterson-uchebnik/22-401"
                    "field_display_title" => "401"
                    "field_outside_task" => null
                    "field_task_type" => Illuminate\Database\Eloquent\Collection {#1095 …2}
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                    "edition_groups" => Illuminate\Database\Eloquent\Collection {#1096 …2}
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                    "parent_branches" => Illuminate\Database\Eloquent\Collection {#1443 …2}
                    "content" => Illuminate\Database\Eloquent\Collection {#1370 …2}
                    "next" => array:2 [ …2]
                    "previous" => array:2 [ …2]
                    "book" => Illuminate\Database\Eloquent\Collection {#1439 …2}
                    "page" => array:2 [ …2]
                  ]
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                  #visible: []
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                    0 => "*"
                  ]
                }
                1 => App\Models\Task {#1402
                  #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" => 2158765
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "field_page_start" => "82"
                    "field_page_end" => null
                    "field_url" => "/5-klass/matematika/peterson-uchebnik/22-402"
                    "field_display_title" => "402"
                    "field_outside_task" => null
                    "field_task_type" => Illuminate\Database\Eloquent\Collection {#1451 …2}
                    "field_metatags_title" => null
                    "field_metatags_description" => null
                    "field_h1" => null
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                    "breadcrumbs" => []
                    "edition_groups" => Illuminate\Database\Eloquent\Collection {#1434 …2}
                    "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1436 …2}
                    "parent_branches" => Illuminate\Database\Eloquent\Collection {#1403 …2}
                    "content" => Illuminate\Database\Eloquent\Collection {#1435 …2}
                    "next" => array:2 [ …2]
                    "previous" => array:2 [ …2]
                    "book" => Illuminate\Database\Eloquent\Collection {#1424 …2}
                    "page" => array:2 [ …2]
                  ]
                  #original: array:24 [
                    "id" => 2158765
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "field_page_start" => "82"
                    "field_page_end" => null
                    "field_url" => "/5-klass/matematika/peterson-uchebnik/22-402"
                    "field_display_title" => "402"
                    "field_outside_task" => null
                    "field_task_type" => Illuminate\Database\Eloquent\Collection {#1451 …2}
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№332 (с. 82)
Условие. №332 (с. 82)
Математика, 5 класс Учебник, авторы: Петерсон Людмила Георгиевна, Дорофеев Георгий Владимирович, издательство Просвещение, Москва, Часть 1, страница 82, номер 332, Условие
Решение. №332 (с. 82)
Математика, 5 класс Учебник, авторы: Петерсон Людмила Георгиевна, Дорофеев Георгий Владимирович, издательство Просвещение, Москва, Часть 1, страница 82, номер 332, Решение

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