Giải phương trình (x - 2022)^3 + (x - 2023)^3 = (2x - 4045)^3
Giải phương trình (x – 2022)3 + (x – 2023)3 = (2x – 4045)3.
(x – 2022)3 + (x – 2023)3 = (2x – 4045)3
⇔ (x – 2022)3 + (x – 2023)3 = [(x – 2022) + (x – 2023)]3
⇔ (x – 2022)3 + (x – 2023)3 = (x – 2022)3 + 3(x – 2022)2(x – 2023) + 3(x – 2022)(x – 2023)2 + (x – 2023)3
⇔ 3(x – 2022)2(x – 2023) + 3(x – 2022)(x – 2023)2 = 0
⇔ 3(x – 2022)(x – 2023)(x – 2022 + x – 2023) = 0
⇔ (x – 2022)(x – 2023)(2x – 4045) = 0
⇔ \(\left[ \begin{array}{l}x - 2022 = 0\\x - 2023 = 0\\2x - 4045 = 0\end{array} \right.\)
⇔ \(\left[ \begin{array}{l}x = 2022\\x = 2023\\x = \frac{{4045}}{2}\end{array} \right.\)
Vậy x ∈ \(\left\{ {2022;2023;\frac{{4045}}{2}} \right\}\).