Olympiad corner selection problem

Algebra Level 5

\[\left\{\begin{matrix} x^3+x(y-z)^2=2 & & \\ y^3+y(z-x)^2=30 & & \\ z^3+z(x-y)^2=16 & & \end{matrix}\right.\] If \(x,y\) and \(z\) satisfy the system of equations above, find the value of \(\left \lfloor 10000(x^4+y^4+z^4) \right \rfloor\).

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