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Консультация № 176917
25.02.2010, 22:46
0.00 руб.
26.02.2010, 11:16
0
1
1
здравствуйте уважаемые эксперты!помогите пожалуйста с заданием:
Обсуждение
Неизвестный
26.02.2010, 04:04
общий
это ответ
Здравствуйте, cookie1992.
(5*x+7)^(1/3)-(5*x-12)^(1/3)=1
Обозначим
u=(5*x+7)^(1/3)
v=(5*x-12)^(1/3)
u-v=1
возведем в куб
(u-v)^3=1^3
u^3-3*u^2*v+3*u*v^2-v^3=1
u^3-v^3-3*u*v(u-v)=1
u^3-v^3=(5*x+7)-(5*x-12)=19 u-v=1
19-3*u*v*1=1
u*v=6 и u-v=1
u=v+1
(v+1)*v=6
v^2+v-6=0
v= -3 и v=2
u= -2 и u=3
u=(5*x+7)^(1/3)= -2 v=(5*x-12)^(1/3)= -3
5*x+7= -8 5*x-12= -27
x= -3 x= -3
u=(5*x+7)^(1/3)= 3 v=(5*x-12)^(1/3)= 2
5*x+7= 27 5*x-12= 8
x=4 x=4
Ответ: x= -3 , x=4
(5*x+7)^(1/3)-(5*x-12)^(1/3)=1
Обозначим
u=(5*x+7)^(1/3)
v=(5*x-12)^(1/3)
u-v=1
возведем в куб
(u-v)^3=1^3
u^3-3*u^2*v+3*u*v^2-v^3=1
u^3-v^3-3*u*v(u-v)=1
u^3-v^3=(5*x+7)-(5*x-12)=19 u-v=1
19-3*u*v*1=1
u*v=6 и u-v=1
u=v+1
(v+1)*v=6
v^2+v-6=0
v= -3 и v=2
u= -2 и u=3
u=(5*x+7)^(1/3)= -2 v=(5*x-12)^(1/3)= -3
5*x+7= -8 5*x-12= -27
x= -3 x= -3
u=(5*x+7)^(1/3)= 3 v=(5*x-12)^(1/3)= 2
5*x+7= 27 5*x-12= 8
x=4 x=4
Ответ: x= -3 , x=4
Форма ответа
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