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I am working on a howework question, trying to prove the following:

$$5a+b > 4\sqrt{ab},$$

where $a$ and $b$ are positive real numbers.

I've tried multiplying expression by $\sqrt{ab}$, squaring both sides of the equation so far. In both cases, after re-factoring, I could not conclude that inequality holds. Can someone point me in the right direction?

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    Use $\frac{5a+b}{2} \geq \sqrt{5ab}$ and also the fact that $\sqrt{5} > 2$ to get the desired result.2012-05-13

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