9. In the ellipse $\Gamma$, $F$ is a focus, and $A, B$ are two vertices. If $|F A|=3,|F B|=2$, find all possible values of $|A B|$.

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Let $F$ be the right focus. When $A, B$ are the left and right vertices, respectively,
$$
\left\{\begin{array} { l } 
{ | F A | = a + c = 3 , } \\
{ | F B | = a - c = 2 }
\end{array} \Rightarrow \left\{\begin{array}{l}
a=\frac{5}{2}, \\
c=\frac{1}{2}
\end{array} \Rightarrow|A B|=2 a=5 ;\right.\right.
$$

When $A$ is the left vertex and $B$ is the upper vertex,
$$
\left\{\begin{array} { l } 
{ | F A | = a + c = 3 , } \\
{ | F B | = a = 2 }
\end{array} \Rightarrow \left\{\begin{array}{l}
a=2, \\
c=1
\end{array} \Rightarrow|A B|=\sqrt{a^{2}+b^{2}}=\sqrt{2 a^{2}-c^{2}}=\sqrt{7} ;\right.\right.
$$

When $A$ is the upper vertex and $B$ is the right vertex,
$$
\left\{\begin{array} { l } 
{ | F A | = a = 3 , } \\
{ | F B | = a - c = 2 }
\end{array} \Rightarrow \left\{\begin{array}{l}
a=3, \\
c=1
\end{array} \Rightarrow|A B|=\sqrt{a^{2}+b^{2}}=\sqrt{2 a^{2}-c^{2}}=\sqrt{17} .\right.\right.
$$

In summary, the possible values of $|A B|$ are $5, \sqrt{7}, \sqrt{17}$.