已知xyz≠0,x≠y,如果(x^2-yz)/[(x(1-yz)]=(y^2-xz)/[y(1-xz)]成立,求证:x+y+z=1/x+1/y+1/z.

问题描述:

已知xyz≠0,x≠y,如果(x^2-yz)/[(x(1-yz)]=(y^2-xz)/[y(1-xz)]成立,求证:x+y+z=1/x+1/y+1/z.