MathDB

4

Part of 2009 German National Olympiad

Problems(1)

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

Source: Germany MO 2009 p4 481344

4/9/2020
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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