# Inspired by Gurido Cuong

Algebra Level 5

$\large \frac{3ab+1}{a+b}+\frac{3bc+1}{b+c}+\frac{3ac+1}{a+c} \geq Kabc$

If $$a,b$$ and $$c$$ are positive real numbers satisfying $$ab+bc+ca=1$$, find the maximum $$K$$ for which the inequality holds.

Inspiration

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