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Консультация № 197706
05.02.2020, 18:53
0.00 руб.
1
1
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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
Решить уравнение.
Указание: сравните множества значений левой и правой частей
уравнения.
Решить уравнение.
Указание: сравните множества значений левой и правой частей
уравнения.
Прикрепленные файлы:
Обсуждение
28.07.2022, 06:55
общий
это ответ
Здравствуйте, Mari!
Рассмотрим левую часть заданного уравнения -- функцию
При
Наименьшее значение функции на этом промежутке достигается при 
причём 
Наибольшего значения у функции на этом промежутке нет.
При
Наименьшее значение функции на этом промежутке достигается при причём 
Наибольшее значение функции на этом промежутке достигается при 
причём 
При
Наименьшее значение функции на этом промежутке достигается при причём 
Наибольшего значения у функции на этом промежутке нет.
Следовательно, левая часть заданного уравнения может принимать значения не меньшие, чем
Рассмотрим правую часть уравнения -- функцию
Эта функция определена при 
Наименьшего значения функция достигает при 
причём 
Наибольшего значения функция достигает при 
причём 
Следовательно, правая часть заданного уравнения может принимать значения от
до 
включительно.
Поскольку обе функции в уравнении должны принимать одно и то же значение, постольку это значение равно Поэтому решение уравнения имеет вид 
Рассмотрим левую часть заданного уравнения -- функцию
При
Наименьшее значение функции на этом промежутке достигается при причём Наибольшего значения у функции на этом промежутке нет.При
Наименьшее значение функции на этом промежутке достигается при причём Наибольшее значение функции на этом промежутке достигается при причём При
Наименьшее значение функции на этом промежутке достигается при причём Наибольшего значения у функции на этом промежутке нет.Следовательно, левая часть заданного уравнения может принимать значения не меньшие, чем
Рассмотрим правую часть уравнения -- функцию
Эта функция определена при Наименьшего значения функция достигает при причём Наибольшего значения функция достигает при причём Следовательно, правая часть заданного уравнения может принимать значения от
до включительно.Поскольку обе функции в уравнении должны принимать одно и то же значение, постольку это значение равно
Поэтому решение уравнения имеет вид
Об авторе:
Facta loquuntur.
Facta loquuntur.
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