2(х²+2х+1)²-(х+1)²=1

Question

2(х²+2х+1)²-(х+1)²=1

Answer 1

2(x²+2x+1)²-(x+1)²=1
2(x+1)⁴-(x+1)²=1
(x+1)² = t,
2t²-t-1=0
D= 1+4*2*1=1+8=9
t₁= 1, t₂= -0,5
(x+1)²=1
x²+2x+1-1=0
x²+2x=0
x(x+2)=0
x₁= 0, x₂=-2
(x+1)²=-0,5
x²+2x+1+0,5=0
x²+2x+1,5=0
D= 4 - 4*1*1,5 = 4-6=-2
D<0,корней нет.<br>Ответ: -2;0.