两边同乘以2并移项得
2x^2+2y^2+2z^2-2xy+2yz+2xz=0
整理得
(x^2-2xy+y^2)+(x^2+2xz+z^2)+(y^2+2yz+z^2)=0
(x-y)^2+(x+z)^2+(y+z)^2=0
得：x-y=0,x+z=0,y+z=0
整理得：x=y=-z
则原命题得证