The basic arithmetic mean-geometric mean (AM-GM) inequality states simply that if x and y are nonnegative real numbers, then. (x+y)/2 ≥ √(x*y), with equality if and only if x = y.
There are various proofs for this theorem (for any number of values), inter alia Polya, Cauchy, by induction etc.
Now derive your proof directly from Pythagoras' formula a²+b² = c², a ≠ b.

(In reply to Solution by Bractals)

Bravo!Excellent work done thats a very nice way to prove the inequality.
I thank you very much for the solution you gave.

Posted by Danish Ahmed Khan on 2012-10-28 06:14:07