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 \(\left \lfloor 10000P \right \rfloor\).


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