Решите уравнение (1-2х)^4-5(1-2x)^2=4

Question

Решите уравнение (1-2х)^4-5(1-2x)^2=4

Answer 1

Замена t=(1-2x)^2, t>=0
t^2-5t-4=0
D=41
t=(5+-sqrt(41))/2
(5-sqrt(41))/2<0 - пост. корень<br>(1-2x)^2=(5+sqrt(41))/2
(1-2x-sqrt((5+sqrt(41))/2))(1-2x+sqrt((5+sqrt(41))/2)=0
x1=(1-sqrt((5+sqrt(41))/2))/2
x2=(1+sqrt((5+sqrt(41))/2))/2