Question 162
Three positive reals $x$, $y$, and $z$ are such that
$$
\begin{aligned}
x^{2}+2(y-1)(z-1) & =85 \\
y^{2}+2(z-1)(x-1) & =84 \\
z^{2}+2(x-1)(y-1) & =89
\end{aligned}
$$
Compute $x+y+z$.
$$
\begin{aligned}
x^{2}+2(y-1)(z-1) & =85 \\
y^{2}+2(z-1)(x-1) & =84 \\
z^{2}+2(x-1)(y-1) & =89
\end{aligned}
$$
Compute $x+y+z$.