Inspired by Daniel Liu

Algebra Level 5

aa+b+bb+c+cc+aKa+b+c\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 KK such that the above inequality holds true for all non-negative values of a,ba, b and cc.

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


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