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Консультация № 191257
02.08.2017, 15:43
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Здравствуйте, уважаемые эксперты! Помогите с задачкой! Заранее благодарю! 
Найдите наименьшее значение выражения |𝑦|+|3𝑥−𝑦|+|𝑥+𝑦−1|, где x и у – произвольные действительные числа.
Найдите наименьшее значение выражения |𝑦|+|3𝑥−𝑦|+|𝑥+𝑦−1|, где x и у – произвольные действительные числа.
Обсуждение
03.08.2017, 10:25
общий
Адресаты:
|y|+|3x−y|+|x+y−1|
А так?
А так?
Об авторе:
"Если вы заметили, что вы на стороне большинства, —
это верный признак того, что пора меняться." Марк Твен
"Если вы заметили, что вы на стороне большинства, —
это верный признак того, что пора меняться." Марк Твен
03.08.2017, 10:55
общий
это ответ
Здравствуйте, Валерий!
При фиксированном значении
заданное выражение имеет значение
не меньше, чем
где
- наименьшее, а 
- наибольшее из чисел 
при этом своё наименьшее значение 
оно принимает при 
равном срединному 
из тех же чисел. В свою очередь, наименьшее значение функции 
достигается при 
и равно 
(см. рисунок ниже).
Похожая задача рассмотрена на странице 299 книги, указанной ниже.
Литература
Хорошилова Е. В. Элементарная математика: Учеб. пособие для старшеклассников и абитуриентов. Часть 1: Теория чисел, алгебра. - М.: Изд-во Моск. ун-та, 2010, 472 с.
При фиксированном значении
заданное выражение имеет значениене меньше, чем
где
- наименьшее, а - наибольшее из чисел при этом своё наименьшее значение оно принимает при равном срединному из тех же чисел. В свою очередь, наименьшее значение функции достигается при и равно (см. рисунок ниже).Похожая задача рассмотрена на странице 299 книги, указанной ниже.
Литература
Хорошилова Е. В. Элементарная математика: Учеб. пособие для старшеклассников и абитуриентов. Часть 1: Теория чисел, алгебра. - М.: Изд-во Моск. ун-та, 2010, 472 с.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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