# 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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