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Консультация № 201371
28.08.2021, 17:24
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6
1
Здравствуйте! У меня возникли сложности с таким вопросом:
Решите уравнение |6x^3+9x-6|=|6x^3+6x^2-13x+6|.
Решите уравнение |6x^3+9x-6|=|6x^3+6x^2-13x+6|.
Обсуждение
28.08.2021, 20:24
общий
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Рассмотрите совокупность уравнений 
и 
Решение заданного уравнения является объединением решений уравнений указанной совокупности.
и Решение заданного уравнения является объединением решений уравнений указанной совокупности.
Об авторе:
Facta loquuntur.
Facta loquuntur.
29.08.2021, 02:43
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Трудность решения - в наличии члена в 3й степени. Но Вы можете легко избавиться от куба, если не поленитесь начертить графики обеих частей уравнения.
На x-интервалах, где функции имеют одинаковый знак, можно просто отбросить модуль-операнды и члены с кубом.
На x-интервалах, где функции имеют разные знаки, можно тоже отбросить модуль-операнды, но все члены отрицательной функции умножьте на (-1). При этом у Вас сократятся свободные члены. Это позволит Вам вынести "x" за скобки и у Вас останется опять же Квадратное уравнение без модулей.
Как решать Квадратное уравнение - см ГорячиеФормулыШкольнойМатематики 301 кБ mathprofi.ru/goryachie_formuly.pdf Ссылка1
См также "Нули функции. Интервалы знакопостоянства функции. Метод интервалов" Ссылка2
На x-интервалах, где функции имеют одинаковый знак, можно просто отбросить модуль-операнды и члены с кубом.
На x-интервалах, где функции имеют разные знаки, можно тоже отбросить модуль-операнды, но все члены отрицательной функции умножьте на (-1). При этом у Вас сократятся свободные члены. Это позволит Вам вынести "x" за скобки и у Вас останется опять же Квадратное уравнение без модулей.
Как решать Квадратное уравнение - см ГорячиеФормулыШкольнойМатематики 301 кБ mathprofi.ru/goryachie_formuly.pdf Ссылка1
См также "Нули функции. Интервалы знакопостоянства функции. Метод интервалов" Ссылка2
29.08.2021, 06:56
общий
29.08.2021, 12:33
это ответ
Здравствуйте, Veterok!
Предлагаю Вам следующее решение задачи.
Заменим заданное уравнение с модулями равносильной совокупностью двух уравнений:
Решим уравнение (1):
кроме того, подстановкой убеждаемся, что
-- корень уравнения (1).
Решим уравнение (2):
отсюда видно, что - корень уравнения (2). Вычислим корни квадратного уравнения в скобках:
Объединив вычисленные корни, получим решение заданного уравнения:
Предлагаю Вам следующее решение задачи.
Заменим заданное уравнение с модулями равносильной совокупностью двух уравнений:
Решим уравнение (1):
кроме того, подстановкой убеждаемся, что
-- корень уравнения (1).Решим уравнение (2):
отсюда видно, что
- корень уравнения (2). Вычислим корни квадратного уравнения в скобках:Объединив вычисленные корни, получим решение заданного уравнения:
Об авторе:
Facta loquuntur.
Facta loquuntur.
29.08.2021, 16:53
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Тут я с вами полностью согласен, третья степень всё осложняет, долго голову ломал над ней.
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