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Консультация № 190049
16.11.2016, 18:53
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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
Как наиболее простым способом вычислить сумму корней этого уравнения |||х-4|-2|-3|-1=0?
Как наиболее простым способом вычислить сумму корней этого уравнения |||х-4|-2|-3|-1=0?
Обсуждение
16.11.2016, 21:03
общий
это ответ
Здравствуйте, svrvsvrv!
Требуется решить уравнение |||x-4|-2|-3| - 1 = 0.
Обозначим z = ||x-4| -2|, y = |x - 4|. Получим уравнения
|z - 3 | =1, |y - 2| = z, |x - 4| = y.
Решаем их последовательно
z1 = 2, z2 = 4.
Для y получим два уравнения:
|y-2| = 2 и |y - 2| = 4.
Первое уравнение дает: y1 = 0, y2 = 4; второе y3 = -2, y4 = 6.
Значение -2 отбрасываем. Для x получим 3 уравнения:
|x - 4| = 0, |x-4| = 4 и |x-4| = 6.
Решения будут такими:
x = 4; x = 0; x = 8; x = 10; x = -2.
Их сумма 4 + 0 + 8 + 10 - 2 = 20.
Требуется решить уравнение |||x-4|-2|-3| - 1 = 0.
Обозначим z = ||x-4| -2|, y = |x - 4|. Получим уравнения
|z - 3 | =1, |y - 2| = z, |x - 4| = y.
Решаем их последовательно
z1 = 2, z2 = 4.
Для y получим два уравнения:
|y-2| = 2 и |y - 2| = 4.
Первое уравнение дает: y1 = 0, y2 = 4; второе y3 = -2, y4 = 6.
Значение -2 отбрасываем. Для x получим 3 уравнения:
|x - 4| = 0, |x-4| = 4 и |x-4| = 6.
Решения будут такими:
x = 4; x = 0; x = 8; x = 10; x = -2.
Их сумма 4 + 0 + 8 + 10 - 2 = 20.
5
Большое Вам спасибо.
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