Question

Prove that for any value of a, b, c; $a^2+b^2+c^2-ab-bc-ca$ is non negative.

Answer 1

$a^2+b^2+c^2-ab-bc-ca=\frac{2(a^2+b^2+c^2-ab-bc-ca)}{2}=\frac{(a^2+b^2-2ab)+(a^2+c^2-2ac)+(b^2+c^2-2bc)}{2}=\frac{(a-b{)}^2+(a-c{)}^2+(b-c{)}^2}{2}>0$

$\therefore$ proved