9. Let $0 \leqslant x_{1} \leqslant x_{2}$, and the sequence $\left\{x_{n}\right\}$ satisfies
$$
x_{n+2}=x_{n+1}+x_{n}(n \geqslant 1) \text {. }
$$

If $1 \leqslant x_{7} \leqslant 2$, then the range of values for $x_{8}$ is
$\qquad$
9. $\left[\frac{21}{13}, \frac{13}{4}\right]$.

From the given information,
$$
\begin{array}{l}
x_{3}=x_{1}+x_{2}, x_{4}=x_{1}+2 x_{2}, x_{5}=2 x_{1}+3 x_{2}, \\
x_{6}=3 x_{1}+5 x_{2}, x_{7}=5 x_{1}+8 x_{2}, x_{8}=8 x_{1}+13 x_{2} .
\end{array}
$$

Since $1 \leqslant x_{7} \leqslant 2$, we have
$$
1 \leqslant 5 x_{1}+8 x_{2} \leqslant 2 \text {. }
$$

Combining $0 \leqslant x_{1} \leqslant x_{2}$, the region enclosed in the $x_{1} O x_{2}$ coordinate system is a quadrilateral, with the coordinates of the four vertices being
$$
\left(0, \frac{1}{8}\right),\left(\frac{1}{13}, \frac{1}{13}\right),\left(\frac{2}{13}, \frac{2}{13}\right),\left(0, \frac{1}{4}\right) \text {. }
$$

Therefore, $x_{8}=8 x_{1}+13 x_{2} \in\left[\frac{21}{13}, \frac{13}{4}\right]$.