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Консультация № 200181
28.01.2021, 18:16
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Здравствуйте! У меня возникли сложности с таким вопросом:
Задание 7. Сколько различных решений имеет уравнение
│x 3 + 47x│= 12x 2 + 60?
Задание 7. Сколько различных решений имеет уравнение
│x 3 + 47x│= 12x 2 + 60?
Обсуждение
28.01.2021, 19:23
общий
это ответ
Здравствуйте, kuznetsova.79!
Обозначим f(x) = |x^3 + 47x| - 12x^2 + 60. При x >= 0 f(x) = x^3 - 12x^2 + 47x - 60 = (x - 5)*(x - 4)*(x - 3),
и уравнение f(x) = 0 имеет три положительных корня. Т.к. f(x) - четная, уравнение f(x) = 0 имеет всего шесть корней.
Обозначим f(x) = |x^3 + 47x| - 12x^2 + 60. При x >= 0 f(x) = x^3 - 12x^2 + 47x - 60 = (x - 5)*(x - 4)*(x - 3),
и уравнение f(x) = 0 имеет три положительных корня. Т.к. f(x) - четная, уравнение f(x) = 0 имеет всего шесть корней.
5
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