Question

已知x2+y2+z2-xy-yz-xz=0,求证x=y=z

Answer 1

x^2+y^2+z^2-xy-xz-yz=0

2x^2+2y^2+2z^2-2xy-2xz-2yz=0

(x^2-2xy+y^2)+(y^2-2yz+z^2)+(x^2-2xz+z^2)=0

(x-y)^2+(y-z)^2+(x-z)^2=0

x=y=z