已知实数xyz满足x/y+z+y/z+x+z/x+y=1求x^2/y+z+y^2/z+x+z^2/x+y的值

因为x/y+z + y/z+x +z/x+y=1 所以x/y+z=1-y/z+x-z/x+y,两边同乘以x 得x^2/y+z=x-xy/z+x-xz/x+y 同理y^2/x+z=y-xy/z+y-yz/x+y,z^2=z-xz/y+z-yz/x+z 原式=x+y+z-(xy+zy)/x+z-(xz+yz)/x+y-(yx+zx)/y+z =x+y+z-y-z-x =0...