# 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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