Đáp án:
$x = -2021;\ x = -\dfrac12$ hoặc $x = 2020$
Giải thích các bước giải:
$\quad (x- 2020)^3 + (x+2021)^3 = (2x +1)^3$
$\Leftrightarrow (x- 2020 +x+2021)^3 - 3(x-2020)(x + 2021)(x - 2020 + x + 2021)= (2x +1)^3$
$\Leftrightarrow (2x+1)^3 - 3(x-2020)(x+2021)(2x+1) = (2x+1)^3$
$\Leftrightarrow (x-2020)(x+2021)(2x+1) = 0$
$\Leftrightarrow \left[\begin{array}{l}x - 2020 = 0\\x + 2021 = 0\\2x +1 = 0\end{array}\right.$
$\Leftrightarrow \left[\begin{array}{l}x = 2020\\x = - 2021\\x = -\dfrac12\end{array}\right.$
Vậy $x = -2021;\ x = -\dfrac12$ hoặc $x = 2020$
