\[\begin{array}{l}
{\text{Решите уравнение:}} \hfill \\
{\left( {x + 1} \right)^5} = 2021 + {x^5}. \hfill \\
\end{array}\]
\[\begin{array}{l}
{\left( {x + 1} \right)^5} = 2021 + {x^5} \Leftrightarrow {\left( {x + 1} \right)^5} - {x^5} - 1 = 2020 \Leftrightarrow 5\left( {{x^2} + x} \right)\left( {{x^2} + x + 1} \right) = 2020 \Leftrightarrow \hfill \\
\left( {{x^2} + x} \right)\left( {{x^2} + x + 1} \right) = 404 \hfill \\
{x^2} + x = t \hfill \\
\end{array}\]
