(1) (x²-1)²-2x²-1=0
(x²-1)²-2(x²-1)-3=0
(x²-1-3)(x²+1)=0,
x²-4=0或x²+1=0(无实数根)
X=±2.
(2) (m²+n²)(m²+n²-2)-8=0
(m²+n²)²-2(m²+n²)-8=0,
(m²+n²-4)(m²+n²+2)=0
m²+n²=4.(m²+n²+2≠0).
⑶（x+1分之1)²-2（x+1分之1）-8=0
(X+1/X-4)(X+1/X+2)=0
X+1/X=4或X+1/X+2=0
X²-4x=-1或X²-2X+1=0
(X-2)²=3或(X-1)²=0
X=1或X=2±√3.
（4）已知x²+y²+4x-6y+13=0,
(X+2)²+(Y-3)²=0
X+2=0且Y-3=0,
X=-2,Y=3,
x+y=1.