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Консультация № 194311
28.12.2018, 15:06
0.00 руб.
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Здравствуйте! Прошу помощи в следующем вопросе:
Найти сумму целых решений неравенства
√(х+1)⩽4-х
Спасибо!
Найти сумму целых решений неравенства
√(х+1)⩽4-х
Спасибо!
Обсуждение
29.12.2018, 04:55
общий
Адресаты:
Графическая иллюстрация. А почему ответ смущает?
Прикрепленные файлы:
31.12.2018, 15:19
общий
это ответ
Здравствуйте, nata!
Пусть требуется вычислить сумму целых решений неравенства
В левой части неравенства находится выражение под знаком квадратного корня. Значение этого выражения не может быть отрицательным. По условию значение выражения в левой части неравенства не превосходит значения выражения в правой части неравенства. Поэтому должны выполняться следующие условия:
или 
или 
В результате числами-кандидатами на решения неравенства являются целые числа, удовлетворяющие условию
Заметим, что при
заданное неравенство становится тождеством, потому что
В левой части заданного неравенства находится возрастающая функция, а в правой части -- убывающая функция. Поэтому целыми решениями неравенства являются числа
Их сумма равна нулю.
Пусть требуется вычислить сумму целых решений неравенства
В левой части неравенства находится выражение под знаком квадратного корня. Значение этого выражения не может быть отрицательным. По условию значение выражения в левой части неравенства не превосходит значения выражения в правой части неравенства. Поэтому должны выполняться следующие условия:
или или В результате числами-кандидатами на решения неравенства являются целые числа, удовлетворяющие условию
Заметим, что при
заданное неравенство становится тождеством, потому чтоВ левой части заданного неравенства находится возрастающая функция, а в правой части -- убывающая функция. Поэтому целыми решениями неравенства являются числа
Их сумма равна нулю.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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