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Приложение: раскрыв скобки получается x^200+(198 положительных членов с x)+1 при x =0 неравенство примет вид 1>=0 что верно любое число меньшее 1 возведенное в степень - меньше 1 равенство верно т.к. 200x^100<1
если числа =1 получаем 200=200 если x>1
левая часть увеличивается за счет положительных членов.
раскрыв скобки получается x^200+(198 положительных членов с x)+1 при x =0 неравенство примет вид 1>=0 что верно любое число меньшее 1 возведенное в степень - меньше 1 равенство верно т.к. 200x^100<1 если числа =1 получаем 200=200 если x>1 левая часть увеличивается за счет положительных членов.
Для того, чтобы обращаться к модераторам, Вы должны знать, чего вы хотите. Насколько я понял, Вы этого не знаете. Не удивляйтесь, если в следующий раз получите предупреждение.
Перемножим скобки в левой части. Получим: (1+x+...+x100) + (x100+x101+...+x200). Объединим члены из двух групп слагаемых попарно в противоположном порядке: (1+x200) +(x+x199)+(x2+x198)+...+ (x100+x100). Произведение слагаемых в каждой из скобок в последнем выражении одинаково и равно x200. Пользуясь тем, что среднее арифметическое больше среднего геометрического или равно ему, находим, что каждая из этих скобок больше или равна 2*x100. Так как всего таких скобок 100, получаем требуемое неравенство.
любое число меньшее 1 возведенное в степень - меньше 1 равенство верно т.к. 200x^100<1
Здесь. как я понимаю, импликация. Если с посылкой еще можно было бы мириться при добавлении условий, которые принимаются автором ответа по умолчанию, т.е. 0<число<1, показатель степени >0, то заключение в общем случае - неверно. Вполне можно подобрать такие x, для которых это условие ложно.
ситуация такая. в мини форум хотел выложить предложение доказательства т.к. оно не совсем красиво получалось, из-за плохой работы интернета получилось положить решение в ответ, поэтому и была прозьба удалить его. но проанализировав ответ, выяснилось что он имеет место жизни с некоторым дополнением, которое написано в мини форуме, поэтому считаю что ответ править не надо.
Об авторе:
to live is to die
Форма ответа
Отправка постов/ответов доступна только зарегистрированным и подтвержденным пользователям.
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