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)=4xy_数学解答

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

人气：320 ℃　时间：2020-07-09 12:14:51

解答

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+...

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