Question 77
Find the maximum value of $z + x$, if $(x, y, z, t)$ satisfies the conditions:
$$
\left\{\begin{array}{l}
x^{2} + y^{2} = 4 \\
z^{2} + t^{2} = 9 \\
x t + y z \geq 6
\end{array}\right.
$$
$$
\left\{\begin{array}{l}
x^{2} + y^{2} = 4 \\
z^{2} + t^{2} = 9 \\
x t + y z \geq 6
\end{array}\right.
$$