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Консультация № 200452
18.03.2021, 15:04
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Здравствуйте, уважаемые эксперты прошу помочь:
найдите наименьшее значение выражения с модулями y=|x-1|+|x-2|+|x-3|+|x-4|
найдите наименьшее значение выражения с модулями y=|x-1|+|x-2|+|x-3|+|x-4|
Обсуждение
18.03.2021, 16:20
общий
это ответ
Здравствуйте, lana-gona!
Чтоб избавиться от заморочных модулей, рассмотрите сначала область x >= 4 . Для этой области можно упростить:
|x-4| = x-4 ; |x-3| = x-3 ; |x-2| = x-2 ; |x-1| = x-1
Затем рассмотрите область 3 <= x < 4 . В ней
|x-4| = -x+4 ; |x-3| = x-3 ; |x-2| = x-2 ; |x-1| = x-1
Затем рассмотрите область 2 <= x < 3 . В ней
|x-4| = -x+4 ; |x-3| = -x+3 ; |x-2| = x-2 ; |x-1| = x-1 , и тд.
В итоге у Вас должно получиться
Ответ : Наименьшее значение выражения = 4.
Чтоб избавиться от заморочных модулей, рассмотрите сначала область x >= 4 . Для этой области можно упростить:
|x-4| = x-4 ; |x-3| = x-3 ; |x-2| = x-2 ; |x-1| = x-1
Затем рассмотрите область 3 <= x < 4 . В ней
|x-4| = -x+4 ; |x-3| = x-3 ; |x-2| = x-2 ; |x-1| = x-1
Затем рассмотрите область 2 <= x < 3 . В ней
|x-4| = -x+4 ; |x-3| = -x+3 ; |x-2| = x-2 ; |x-1| = x-1 , и тд.
В итоге у Вас должно получиться
Ответ : Наименьшее значение выражения = 4.
5
спасибо
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