Task 1. (5 points) Solve the equation $x^{6}-2020 x^{2}-\sqrt{2021}=0$.

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Solution.

Rewrite the equation as $x^{6}-2021 x^{2}+x^{2}-\sqrt{2021}=0$. Then

$$
\begin{aligned}
& x^{2}\left(x^{4}-2021\right)+\left(x^{2}-\sqrt{2021}\right)=0, \\
& x^{2}\left(x^{2}-\sqrt{2021}\right)\left(x^{2}+\sqrt{2021}\right)+\left(x^{2}-\sqrt{2021}\right)=0, \\
& \left(x^{2}-\sqrt{2021}\right)\left(x^{4}+x^{2} \sqrt{2021}+1\right)=0, \\
& x^{2}-\sqrt{2021}=0, \text { or } x^{4}+x^{2} \sqrt{2021}+1=0, \\
& x_{1,2}= \pm \sqrt[4]{2021} ; \\
& \text { since } \frac{-\sqrt{2021} \pm \sqrt{2017}}{2}<0 \text {, the equation } x^{2}-\frac{-\sqrt{2021} \pm \sqrt{2017}}{2}=0 \text { has no real }
\end{aligned}
$$

roots.

Answer. $\{ \pm \sqrt[4]{2021}\}$.