题目所给条件不够明白,如为 x+(1/y)=y+(1/z)=z+(1/x),则：
x-y=(1/z)-(1/y)=(y-z)/(yz),y-z=(1/x)-(1/z)=(z-x)/(zx),z-x=(1/y)-(1/x)=(x-y)/(xy)；
于是 (x-y)(y-z)(z-x)=[(y-z)/(yz)]*[(z-x)/(zx)]*[(x-y)/(xy)]；
因 x≠y≠z,故 1=1/(xyz)²,即 x²y²z²=1；