Question 4
Let $x$, $y$, and $z$ be real numbers that satisfy the following system:
$$
\begin{aligned}
x+3y+6z &= 1 \\
xy+2xz+6yz &= -8 \\
xyz &= 2
\end{aligned}
$$
Find the smallest possible value of $x+y+z$.
$$
\begin{aligned}
x+3y+6z &= 1 \\
xy+2xz+6yz &= -8 \\
xyz &= 2
\end{aligned}
$$
Find the smallest possible value of $x+y+z$.