Question

配方法解 x2+1/x2-x-1/X-4=0

Answer 1

令a=x-1/x

a²=x²-2+1/x²

x²+1/x²=a²+2

所以a²+2-a-4=0

a²-a=2

a²-a+1/4=9/4

(a-1/2)²=(±3/2)²

a-1/2=±3/2

a=-1,a=2

x-1/x=-1

x²+x=1

(x+1/2)²=5/4

x+1/2=±√5/2

x-1/x=2

x²-2x=1

(x-1)²=2

x-1=±√2

所以

x=(1-√5)/2

x=(1+√5)/2

x=1-√2

x=1+√2