Polynomial Diophantine Equation 2

\[\large x^8+6x^4y^2+ y^4=2z^2\]

Let \(1\leq x,y,z\leq 5000 \) be positive integers satisfying the equation above.

Evaluate \(\max(x+y+z) \)


This is a part of the set Polynomial Diophantine Equations

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