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Консультация № 195452
02.05.2019, 00:28
0.00 руб.
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1
Здравствуйте! Прошу помощи в следующем вопросе:
Среди чисел a, b, c есть числа разных знаков. Доказать, что
2(ab+ac+cb)<a^2+b^2+c^2
Среди чисел a, b, c есть числа разных знаков. Доказать, что
2(ab+ac+cb)<a^2+b^2+c^2
Обсуждение
02.05.2019, 10:28
общий
это ответ
Здравствуйте, Valentin!
Примем для определённости, что
или 
Пусть
Тогда из заданного неравенства получим, что
это верно, так как
Пусть
Тогда из заданного неравенства получим, что
это верно, так как
Пусть
Тогда из заданного неравенства получим, что
это верно, так как
Рассмотрите, пожалуйста, самостоятельно остальные случаи.
Примем для определённости, что
или Пусть
Тогда из заданного неравенства получим, чтоэто верно, так как
Пусть
Тогда из заданного неравенства получим, чтоэто верно, так как
Пусть
Тогда из заданного неравенства получим, чтоэто верно, так как
Рассмотрите, пожалуйста, самостоятельно остальные случаи.
5
Об авторе:
Facta loquuntur.
Facta loquuntur.
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