Đáp án:
$\begin{array}{l}
A = {2020^{100}} + {2020^{96}} + {2020^{92}} + ... + {2020^4}\\
\Rightarrow {2020^4}.A = {2020^{104}} + {2020^{100}} + ... + {2020^8}\\
\Rightarrow {2020^4}.A - A = {2020^{104}} - {2020^4}\\
\Rightarrow A = \dfrac{{{{2020}^{104}} - {{2020}^4}}}{{{{2020}^4} - 1}}\\
\Rightarrow {2020^{100}} + {2020^{96}} + {2020^{92}} + ... + {2020^4} + 1\\
= \dfrac{{{{2020}^{104}} - {{2020}^4}}}{{{{2020}^4} - 1}} + 1\\
= \dfrac{{{{2020}^{104}} - {{2020}^4} + {{2020}^4} - 1}}{{{{2020}^4} - 1}}\\
= \dfrac{{{{2020}^{104}} - 1}}{{{{2020}^4} - 1}}\\
\Rightarrow \dfrac{{\left( {{{2020}^{100}} + {{2020}^{96}} + {{2020}^{92}} + ... + {{2020}^4} + 1} \right)}}{{\left| {x - 2020} \right|}}\\
= \dfrac{{{{2020}^{104}} - 1}}{{{{2020}^4} - 1}}\\
\Rightarrow \dfrac{{{{2020}^{104}} - 1}}{{{{2020}^4} - 1}}.\dfrac{1}{{\left| {x - 2020} \right|}} = \dfrac{{{{2020}^{104}} - 1}}{{{{2020}^4} - 1}}\\
\Rightarrow \dfrac{1}{{\left| {x - 2020} \right|}} = 1\\
\Rightarrow \left| {x - 2020} \right| = 1\\
\Rightarrow \left[ \begin{array}{l}
x - 2020 = 1\\
x - 2020 = - 1
\end{array} \right.\\
\Rightarrow \left[ \begin{array}{l}
x = 2021\\
x = 2019
\end{array} \right.\\
Vậy\,x = 2021;x = 2019
\end{array}$
