Ta có: x^2 + y^2 + z^2 = xy+xz+yz
=> 2x^2+2y^2+2z^2-2xy-2yz-2xz=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
Mà (x-y)^2 \geq 0 (mọi x,y)
(y-z)^2 \geq 0 (mọi y,z)
(x-z)^2 \geq 0 (mọi x,z)
Nên \left\{\begin{matrix} x-y=0 \\ y-z=0 \\ z-x=0 \end{matrix}\right.
=>...