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Консультация № 177288
16.03.2010, 20:53
43.65 руб.
0
1
1
Добрый вечер, уважаемые Эксперты)
Помогите, пожалуйста, с решением системы:
| log2( 3-[$8730$](x-2y) )= 1-log4y
| xy2 = 2y3+1
Спасибо за уделенное время )
Помогите, пожалуйста, с решением системы:
| log2( 3-[$8730$](x-2y) )= 1-log4y
| xy2 = 2y3+1
Спасибо за уделенное время )
Обсуждение
Неизвестный
16.03.2010, 21:07
общий
это ответ
Здравствуйте, Schuldig.
Из второго уравнения выражаем x
x=(2y3+1)/y2
Подставляем в первое уравнение
log2( 3-√((2y3+1)/y2-2y) )= 1-log4y
log2( 3-√((2y3+1-2y3)/y2 )= log22-log2y1/2
log2( 3-√(1/y2 )= log2(2/y1/2)
Так как y>0, то [$8730$]y2=y
3-1/y=2/[$8730$]y
Заменим 1/[$8730$]y=t>0
3-t2=2t
t2+2t-3=0
t=-3 - посторонний
t=1
1/[$8730$]y=1
y=1
Тогда x=(2y3+1)/y2=(2+1)/1=3
Из второго уравнения выражаем x
x=(2y3+1)/y2
Подставляем в первое уравнение
log2( 3-√((2y3+1)/y2-2y) )= 1-log4y
log2( 3-√((2y3+1-2y3)/y2 )= log22-log2y1/2
log2( 3-√(1/y2 )= log2(2/y1/2)
Так как y>0, то [$8730$]y2=y
3-1/y=2/[$8730$]y
Заменим 1/[$8730$]y=t>0
3-t2=2t
t2+2t-3=0
t=-3 - посторонний
t=1
1/[$8730$]y=1
y=1
Тогда x=(2y3+1)/y2=(2+1)/1=3
5
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