Algebra vs. Trigonometry

Algebra Level 5

P=x2+7yz22z\large P=x^{2}+\sqrt{7y}-z^2-2z

Given that x,yx,y and zz are real numbers satisfying xy1(z+1)=yz2+2yz2z24zx-\sqrt{y-1}(z+1)=\sqrt{yz^2+2yz-2z^2-4z} and y2y\le2, determine the maximum value of PP.

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