1. Solution. The inequality is equivalent to

$$
\begin{aligned}
& \sqrt{9-x} \cdot\left(\left|x^{2}-10 x+13\right|-\left|x^{2}-1\right|\right) \geqslant 0 \Longleftrightarrow \\
& \sqrt{9-x} \cdot\left(x^{2}-10 x+13-x^{2}+1\right)\left(x^{2}-10 x+13+x^{2}-1\right) \geqslant 0 \Longleftrightarrow \\
& \sqrt{9-x} \cdot(-5 x+7)\left(x^{2}-5 x+6\right) \geqslant 0 \Longleftrightarrow \\
& \sqrt{9-x} \cdot(x-7 / 5)(x-2)(x-3) \leqslant 0
\end{aligned}
$$
Answer: $(-\infty ; 7 / 5] \cup[2 ; 3] \cup\{9\}$ (variant $2-2:(-\infty ; 15 / 7] \cup[3 ; 4] \cup\{7\})$.