Question

Решите уравнение (x^2 + 2x)^2-2(x+1)^2=1

 

Answer 1

(x^2 + 2x)^2-2(x+1)^2=1,

(x^2 + 2x)^2-2(x^2+2x+1)-1=0,

(x^2 + 2x)^2-2(x^2+2x)+2-1=0,

(x^2 + 2x)^2-2(x^2+2x)+1=0,

x^2+2x=t,

t^2-2t+1=0,

(t-1)^2=0,

t-1=0,

t=1,

x^2+2x=1,

x^2+2x-1=0,

D1=2,

x1=-1-√2,

x2=-1+√2