令t=x+1/x
则t^2=x^2+2+1/x^2
所以x^2+1/x^2=t^2-2
x^3+1/x^3=(x+1/x)(x^2-1+1/x^2)=2
所以t(t^2-2-1)=t^3-3t=2
t^3-3t-2=0
(t^3+1)-3t-3=0
(t+1)(t^2-t+1)-3(t+1)=0
(t+1)(t^2-t+1-3)=0
(t+1)(t^2-t-2)=0
(t+1)^2(t-2)=0
t=-1,t=2
因为x^3和1/x^3同号
相加大于0,所以x^3>0
x>0
所以x+1/x>0
所以x+1/x=2