2007 Indonesia MO Problems/Problem 3
Let be positive real numbers which satisfy . Prove that these three inequalities hold: , , .
Solution (credit to vedran6)
Assume that , so . Let , making . Therefore, .
By substitution, we have Note that because , we must have . Additionally, by the Trivial Inequality, . Thus, we must have , is a contradiction. Therefore, we must have .
Because of symmetry in the equation, we can use similar steps to prove that and that .
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