2(x²+1/x²）-3（x+1/x）-1=0

2(x²+1/x²）-3（x+1/x）-1=0
2(x²+1/x²）-3（x+1/x）-1=0

2(x²+1/x²）-3（x+1/x）-1=0
2(x²+1/x²)-3（x+1/x）-1=0
设t=x+1/x
x²+1/x²=(x+1/x)²-2=t²-2
2(t²-2)-3t-1=0
2t²-3t-5=0
(2t-5)(t+1)=0
t1=5/2 t2=-1
x+1/x=5/2
2x²+2=5x
2x²-5x+2=0
(2x-1)(x-2)=0
x1=1/2 x2=2
x+1/x=-1
x²+1=-x
x²+x+1=0
无解
所以x1=1/2 x2=2