# AM-GM might help out

Algebra Level 4

If $$\displaystyle x,y,z\in\mathbb R$$ are positive, solve $\displaystyle\begin{cases}x+\frac{1}{yz}+z^2=3\\y+\frac{1}{xz}=2\end{cases}$

The solutions are $$\displaystyle (x_1,y_1,z_1), (x_2,y_2,z_2),\ldots, (x_n,y_n,z_n)$$.

Find $$\displaystyle\sum_{i=1}^n (x_i+y_i+z_i)$$.

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