已知x+1/y=y+1/z=z+1/x,求证y/x+z/y+x/z=3 ,
问题描述：
已知x+1/y=y+1/z=z+1/x,求证y/x+z/y+x/z=3 ,
答
x+1/y=y+1/z=z+1/x=kzx+z/y=kz => z/y=kz-zxxy+x/z=kx => x/z=kx-xyyz+y/x=ky => z/y=ky-zyy/x+z/y+x/z = k(x+y+z)-xy-yz-xz又因为xy+1=ky => 1=ky-xyyz+1=kz => 1=kz-yzzx+1=kx => 1=kx-zx所以y/x+z/y+x/z=3