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Консультация № 199736
28.11.2020, 13:07
0.00 руб.
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Найти сумму корней или корень (если он единственный)
уравнения:
(x(x+2))/(2/(x-8)-1/(x-5))=8/(2/(x-8)+1/(5-x))
Найти сумму корней или корень (если он единственный)
уравнения:
(x(x+2))/(2/(x-8)-1/(x-5))=8/(2/(x-8)+1/(5-x))
Прикрепленные файлы:
Обсуждение
30.11.2020, 16:31
общий
это ответ
Здравствуйте, Barsik22!
Дано уравнение x·(x+2) / [2 / (x-8) - 1 / (x-5)] = 8 / [2 / (x-8) + 1 / (5-x)]
Вычислить сумму корней этого уравнения.
Решение : Область определения заданного уравнения - вся числовая ось кроме x=8 и x=5 , потому что в знаменателях присутствуют разности (x-8) и (x-5) , а на нуль делить нельзя.
Это ограничение позволяет разделить обе части уравнения на (x-8)·(x-5) , не равное нулю. То есть умножим оба знаменателя больших дробей на (x-8)·(x-5) .
Дальнейшие вычисления и проверку я показал на ниже-скриншоте.
Ответ : уравнение имеет единственный корень x = -4 .
Дано уравнение x·(x+2) / [2 / (x-8) - 1 / (x-5)] = 8 / [2 / (x-8) + 1 / (5-x)]
Вычислить сумму корней этого уравнения.
Решение : Область определения заданного уравнения - вся числовая ось кроме x=8 и x=5 , потому что в знаменателях присутствуют разности (x-8) и (x-5) , а на нуль делить нельзя.
Это ограничение позволяет разделить обе части уравнения на (x-8)·(x-5) , не равное нулю. То есть умножим оба знаменателя больших дробей на (x-8)·(x-5) .
Дальнейшие вычисления и проверку я показал на ниже-скриншоте.
Ответ : уравнение имеет единственный корень x = -4 .
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