已知xyz满足z+y+z=xyz 求证：
问题描述：
已知xyz满足z+y+z=xyz 求证：
x(1-y2)(1-z2)+y(1-x2)(1-z2)+z(1-x2)(1-y2)=4xyz
答
x(1-y²)(1-z²)+y(1-x²)(1-z²)+z(1-x²)(1-y²)=x(1-y²-z²+y²z²)+y(1-x²-z²+x²z²)+z(1-x²-y²+x²y²)=x-xy²-xz²+...