Difference between revisions of "2010-2011 Mock USAJMO Problems/Solutions/Problem 2"
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Revision as of 17:34, 24 April 2012
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 .