Inspired by Daniel Liu

Algebra Level 5

\[\frac{a}{\sqrt{a+b}}+\frac{b}{\sqrt{b+c}}+\frac{c}{\sqrt{c+a}}\leq K\sqrt{a+b+c}\]

Find the smallest value of \(K\) such that the above inequality holds true for all non-negative values of \(a, b \) and \(c\).

What is \( \left \lfloor 10000K \right \rfloor?\)


Inspiration

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