2. Solve the inequality $\frac{\sqrt{x^{6}-21}}{x^{3}}-\frac{x^{3}}{\sqrt{x^{6}-21}}<\frac{21}{10}$.
# Solution:

Domain of definition: $|x|>\sqrt[6]{21} . \frac{\sqrt{x^{6}-21}}{x^{3}}-\frac{x^{3}}{\sqrt{x^{6}-21}}\sqrt[6]{21}$ inequality is true.
2) For $x10$, or $\left(-x^{3} \sqrt{x^{6}-21}\right)^{2}>100$,

$$
\begin{aligned}
& x^{12}-21 x^{6}-100>0,\left(x^{6}+4\right)\left(x^{6}-25\right)>0,\left(x^{3}+5\right)\left(x^{3}-5\right)>0 . \text { Since } x<-\sqrt[6]{21}, \text { then } \\
& x<-\sqrt[3]{5}
\end{aligned}
$$

Answer: $x \in(-\infty ;-\sqrt[3]{5}) \cup(\sqrt[6]{21} ;+\infty)$.