若a/x^2-yz=b/y^2-zx=c/z^2-xy,求证ax+by+cz=(a+b+c)(x+y+z)
问题描述:
若a/x^2-yz=b/y^2-zx=c/z^2-xy,求证ax+by+cz=(a+b+c)(x+y+z)
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...