Question

Prove that a²+b²+c²-ab-bc-ca is always non negative for all values of A, B and C.

Answer 1

a2 + b2 +c2 - ab - bc - ca
2/2(a2 + b2 +c2 - ab - bc - ca)
1/2(2a2 + 2b2 +2c2 - 2ab - 2bc - 2ca)
1/2(a2 + b2 - 2ab +b2 +c2 - 2bc + c2 + a2 - ca)
1/2[(a - b)square + (b - c)square + (c - a)square]

As squares of any real numbers can't be negative, therefore is always non negative for all values of a, b, c.

Answer 2

Please see below

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