Question 48
Given positive real numbers $x$, $y$, and $z$ that satisfy the following system of equations:
$$
\begin{aligned}
x^{2}+y^{2}+x y &=1, \\
y^{2}+z^{2}+y z &=4, \\
z^{2}+x^{2}+z x &=5,
\end{aligned}
$$
find $x+y+z$.
$$
\begin{aligned}
x^{2}+y^{2}+x y &=1, \\
y^{2}+z^{2}+y z &=4, \\
z^{2}+x^{2}+z x &=5,
\end{aligned}
$$
find $x+y+z$.