# A Beautiful but Difficult Inequality

Algebra Level 5

$\dfrac{x}{\sqrt{x+y}}+\dfrac{y}{\sqrt{y+z}}+\dfrac{z}{\sqrt{z+x}}$

Over all non-negative reals $$x, y, z$$ satisfying $$x + y + z = 4$$, let the maximium value of the above expression be $$M$$. What is the value of $$\lfloor 10000 \times M \rfloor$$?

×