Question

Срочно!!! Решить ур-е 1/х(х-2) + 2/(х-1)^2=2

Answer 1

1/x(x-2)+2/(x-1)^2=2
x-1=t
1/(t^2-1)+2/t^2=2
t^2+2t^2-2=2t^4-2t^2
2t^4-5t^2+2=0
t^2=(5+-3)/4
t^2(1)=2
t^2(2)=1/2

x=1+t

t1=sqrt(2)  x1=1+√2
t2=-sqrt(2)  x2=1-√2
t3=√2/2       x3=1+√2/2
t4=-√2/2      x4=1-√2/2