令a=x+1/x
则a²=x²+2+1/x²
x²+1/x²=a²-2
x³+1/x³
=(x+1/x)(x²-1+1/x²)
=a(a²-2-1)
=a³-3a
所以即a³-3a+6=2a²
a³-2a²-3a+6=0
a²(a-2)-3(a-2)=0
(a-2)(a²-3)=0
a=2,a=±√3
x+1/x=±√3时
即x²±√3x+1=0
此时判别式小于0
没有实数解
所以x+1/x=2