巧解方程(1) (x²-1)²-2x²-1=0 (2) (m²+n²)
1个回答

(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.