Question

If a=87, b=85 and c=83, then the value of a^2 + b^2 + c^2 ab bc ca is

Answer 1

By an identity,
$a {}^{2} + b{}^{2} + c{}^{2} - ab - bc - ac = \frac{1}{2} (( {a - b)}^{2} + ( {b - c)}^{2} + ( {c - a)}^{2} )$
So putting values of a, b and c, we get,
1/2.2^2.2^2.(-2)^2=32