x+(1/y)=y+(1/z)=z+(1/x) x不等于z不等于y 求证x^2y^2z^2=1
问题描述：
x+(1/y)=y+(1/z)=z+(1/x) x不等于z不等于y 求证x^2y^2z^2=1
周日截止！
答
因为x+1/y=y+1/z所以x-y=1/z-1/y即x-y=(y-z)/yz
同理y-z=(z-x)/xz,z-x=(x-y)/xy
所以x-y=(y-z)/yz=(z-x)/xyz^2=(x-y)/x^2y^2z^2
又x不等于y不等于z,即x-y不为0
所以x^2y^2z^2=1如何得x-y=(y-z)/yz=(z-x)/xyz^2=(x-y)/x^2y^2z^2？具体点！x+(1/y)=y+(1/z)移项x-y=(1/z)-(1/y) 通分x-y =(y-z)yz那又怎么得(y-z)/yz=(z-x)/xyz^2=(x-y)/x^2y^2z^2？在具体点！在线等，快把y-z=(z-x)/xzz-x=(x-y)/xy代入所以x-y= (y-z)/yz=[(z-x)/xz]/yz= (z-x)/xyz^2=(x-y)/x^2y^2z^2