# Algebra vs. Trigonometry

Algebra Level 5

$\large P=x^{2}+\sqrt{7y}-z^2-2z$

Given that $$x,y$$ and $$z$$ are real numbers satisfying $x-\sqrt{y-1}(z+1)=\sqrt{yz^2+2yz-2z^2-4z}$ and $$y\le2$$, determine the maximum value of $$P$$.

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