# Getting started part II

Algebra Level 4

$\left\{\begin{matrix} x-y+z=3 & & \\ x^2+y^2+z^2=5 & & \end{matrix}\right.$ Let $$x,y$$ and $$z$$ be real numbers satisfying the system of equations above, find the product of minimum and maximum of the expression below: $P=\frac{x+y-2}{z+2}.$

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