Question

Prove that x^2+y^2+z^2-xy-yz-zx is always positive

Answer 1

$x^2+y^2+z^2-xy-yz-zx\\ =2(x^2+y^2+z^2-xy-yz-zx)/2 \\ = (2x^2+2y^2 +2z^2-2xy-2yz-2zx)/2\\ = ((x-y)^2 + (y-z)^2 + (z-x)^2)/2$
Since square of all numbers are positive, so, it will always be positive number.