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1 /sqrt{x}} 1/ \sqrt{a+b-x} < 1/\sqrt{a} + 1 / \sqrt{b}

Source: Germany MO 2009 p4 481344

April 9, 2020
inequalitiesInequalityalgebraradical

Problem Statement

Let aa and bb be two fixed positive real numbers. Find all real numbers xx, such that inequality holds 1x+1a+b−x<1a+1b\frac{1}{\sqrt{x}}+\frac{1}{\sqrt{a+b-x}} < \frac{1}{\sqrt{a}} + \frac{1}{\sqrt{b}}
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