2010-2011 Mock USAJMO Problems/Solutions/Problem 2
Problem 2
Let be positive real numbers such that . Prove that with equality if and only if .
Solution 1
First, we change the terms using the relationship :
Then, by Cauchy-Schwarz Inequality, one has:
And by AM-GM, one has:
Therefore,
where both equations are true if and only if .
edited by User:lightest 17:35, 24 April 2012 (EDT)