1/x=-x^2+2x
x^2-2x+1/x=0
x^3-2x^2+1=0
x^2(x-1)-(x^2-1)=0
x^2(x-1)-(x+1)(x-1)=0
(x^2-x-1)(x-1)=0
若x^2-x-1=0 解得x=(1±√5)/2
若x-1=0 解得x=1
所以交点个数为3
分别为(1,1) ((1+√5)/2,(√5-1)/2) ((1-√5)/2,-(√5+1)/2)