# Fun with Cyclic

Algebra Level 5

Let $$f(a,b,c)=$$$$(\sqrt{a+b+c})(\sum_{cyc}\frac{\sqrt{a+b+c}+\sqrt{a}}{b+c})$$

Find the minimum value of $$f(a,b,c)$$ upto $$3$$ decimal places, as $$a,b,c$$ varies over all positive reals.

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