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Консультация № 189753
10.09.2016, 21:44
0.00 руб.
1
2
2
Здравствуйте! У меня возникли сложности с такой задачей ( № 2 ) :
Прикрепленные файлы:
Обсуждение
11.09.2016, 07:57
общий
это ответ
Здравствуйте, anton74551!
Рассмотрим первое уравнение. Имеем
При
условие 
выполняется, а при 
не выполняется. Значит, заданное уравнение имеет одно решение: 
Рассмотрим первое уравнение. Имеем
При
условие выполняется, а при не выполняется. Значит, заданное уравнение имеет одно решение:
Об авторе:
Facta loquuntur.
Facta loquuntur.
11.09.2016, 10:49
общий
это ответ
Здравствуйте, anton74551!
б) 18/(x-5)[sup]2[/sup] + 15/((x-1)(x-9)) = 5/(x[sup]2[/sup] - 10x -7).
Раскроем скобки в знаменателях
18/(x2-10x+25) + 15/((x2-10x+9)) = 5/(x2 - 10x -7)
и сделаем замену t = x2 - 10x.
После подстановки имеем
18/(t +25) + 15/(t + 9) = 5/(t-7).
Приводим дроби к общему знаменателю (t+25)(t+9)(t-7) и приравняем числители,
получим уравнение
18*(t+9)(t-7) + 15*(t+25)(t-7) = 5*(t+25)(t+9),
или
7*t2 + 34t - 1221 = 0,
корни которого t1 = - 111/7, t2 = 11.
Для x имеем два уравнения:
x2 - 10x - 11 = 0 и 7x2 - 70x + 111 = 0.
Их корни
x1 = 11, x2 = -1, x3,4 = -5[$177$](8/7)*[$8730$]7 .
Все они являются решениями данного в задаче уравнения, т.к.
не обращают в нуль ни один из знаменателей дробей.
б) 18/(x-5)[sup]2[/sup] + 15/((x-1)(x-9)) = 5/(x[sup]2[/sup] - 10x -7).
Раскроем скобки в знаменателях
18/(x2-10x+25) + 15/((x2-10x+9)) = 5/(x2 - 10x -7)
и сделаем замену t = x2 - 10x.
После подстановки имеем
18/(t +25) + 15/(t + 9) = 5/(t-7).
Приводим дроби к общему знаменателю (t+25)(t+9)(t-7) и приравняем числители,
получим уравнение
18*(t+9)(t-7) + 15*(t+25)(t-7) = 5*(t+25)(t+9),
или
7*t2 + 34t - 1221 = 0,
корни которого t1 = - 111/7, t2 = 11.
Для x имеем два уравнения:
x2 - 10x - 11 = 0 и 7x2 - 70x + 111 = 0.
Их корни
x1 = 11, x2 = -1, x3,4 = -5[$177$](8/7)*[$8730$]7 .
Все они являются решениями данного в задаче уравнения, т.к.
не обращают в нуль ни один из знаменателей дробей.
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