Let be positive real numbers such that

Prove that

*(Vojtech Jarnik / Second Category / 2016)*

**Solution**

Using the AM – GM inequality we have that

as well as . Thus:

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# An inequality

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Let be positive real numbers such that

Prove that

*(Vojtech Jarnik / Second Category / 2016)*

**Solution**

Using the AM – GM inequality we have that

as well as . Thus: