若a/x^2-yz=b/y^2-zx=c/z^2-xy,求证ax+by+cz=(a+b+c)(x+y+z)
人气：456 ℃ 时间：2020-05-06 10:20:57
解答
设a/x^2-yz=b/y^2-zx=c/z^2-xy=k则a=k（x^2-yz）b=k（y^2-zx）c=k（z^2-xy）带入待证式子：k（x^2-yz）x+k（y^2-zx）y+k（z^2-xy）z=k（x^3+y^3+z^3-3xyz)右=k（x^2+y^2+z^2-xy-yz-xz）*（x+y+z）即证+x^3+y^3+z^3-3...
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