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Консультация № 195537
06.05.2019, 01:31
0.00 руб.
07.05.2019, 19:09
1
1
1
Здравствуйте! У меня возникли сложности с таким вопросом:
Решить уравнение
Решить уравнение
Прикрепленные файлы:
Обсуждение
09.05.2019, 10:25
общий
это ответ
Здравствуйте, svrvsvrv!
Присутствие корня четной степени несет ограничение на область допустимых значений переменной х.
Теперь, найдя область определения, подметим, что при
, получаем верное равенство. Значит корень уравнения.
Рассмотрим другие случаи, если
. Разделим левую и правую часть на 
Это равенство может быть справедливо при
Возведем в квадрат левую и правую часть уравнения. Получим
При новой области допустимых значений переменной внутренность модуля всегда будет положительной, поэтому
Заметим, что для решения этого нового уравнения область определения сужается
Решая уравнение, получаем
, и 
, где последний корень в данном случае посторонний 
Подведем итоги.
и полученный предыдущий корень
Присутствие корня четной степени несет ограничение на область допустимых значений переменной х.
Теперь, найдя область определения, подметим, что при
, получаем верное равенство. Значит корень уравнения.Рассмотрим другие случаи, если
. Разделим левую и правую часть на Это равенство может быть справедливо при
Возведем в квадрат левую и правую часть уравнения. Получим
При новой области допустимых значений переменной внутренность модуля всегда будет положительной, поэтому
Заметим, что для решения этого нового уравнения область определения сужается
Решая уравнение, получаем
, и , где последний корень в данном случае посторонний Подведем итоги.
и полученный предыдущий корень
5
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