Question 2
Determine the largest real number $z$ such that
$$
\begin{gathered}
x + y + z = 5 \\
x y + y z + x z = 3
\end{gathered}
$$
and $x$, $y$ are also real.
$$
\begin{gathered}
x + y + z = 5 \\
x y + y z + x z = 3
\end{gathered}
$$
and $x$, $y$ are also real.