Difference between revisions of "2006 IMO Shortlist Problems/A4"
(New page: == Problem == Prove the inequality <cmath> \sum_{i<j} \frac{a_ia_j}{a_i+a_j} \le \frac{n}{2(a_1 + a_2 + \dotsb a_n)} \sum_{i<j} a_i a_j </cmath> for positive real numbers <math>a_1, \dots...) |
(No difference)
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Revision as of 11:46, 29 December 2007
Problem
Prove the inequality for positive real numbers .
Solution
Note that Suppose that . Note that is an increasing function of both and . It follows that if , then i.e., is an increasing function of .