# Another inequality

Algebra Level 4

$\large \sqrt{a + \dfrac{1}{a} } + \sqrt{b+ \dfrac{1}{b}} + \sqrt{c + \dfrac{1}{c}} \geq S (\sqrt{a} + \sqrt{b} + \sqrt{c})$

Let $a,b$ and $c$ be positive numbers satisfying $ab+bc+ac=1$. Find the largest value of $S$ for the inequality above

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