2. Solve the inequality $\sqrt{x^{2}-1} \leqslant \sqrt{5 x^{2}-1-4 x-x^{3}}$.
Answer: $(-\infty ;-1] \cup\{2\}$.

Solution. $\sqrt{x^{2}-1} \leqslant \sqrt{5 x^{2}-1-4 x-x^{3}} \Leftrightarrow 0 \leqslant x^{2}-1 \leqslant 5 x^{2}-1-4 x-x^{3} \Leftrightarrow$

$$
\Leftrightarrow\left\{\begin{array}{l}
x \in(-\infty ;-1] \cup[1 ;+\infty), \\
x(x-2)^{2} \leqslant 0
\end{array} \Leftrightarrow x \in(-\infty ;-1] \cup\{2\}\right.
$$