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！

Question

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！

Answer 1

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