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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