Prove that a 2 + b 2 + c 2 – ab – bc – ca is always non-negative for all values of a, b and c.

Question

Prove that a 2 + b 2 + c 2 &#x2013; ab &#x2013; bc &#x2013; ca is always non-negative for all values of a, b and c.

Philoid · Accepted Answer

We have to prove that a²+ b²+c²–ab–bc–ca 0

Lets us consider,