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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