# Problem 1

Algebra Level 5

$\frac{x^2}{y+2z}+\frac{y^2}{z+2x}+\frac{z^2}{x+2y}$

Given that $$x$$, $$y$$ and $$z$$ are positive reals which satisfy $$3(x^4+y^4+z^4)-7(x^2+y^2+z^2)=-12$$. Let the minimum value of the expression above be $$P$$. Find $$\left \lfloor 10000P \right \rfloor$$.

This problem is in this set.

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