Question

[Han Han]

(x-5) mũ 2022 = (x -5 ) mũ 2024

Answer 1

[⭐Hannie⭐]

\(\left(x-5\right)^{2022}=\left(x-5\right)^{2024}\\ \Rightarrow\left(x-5\right)^{2022}-\left(x-5\right)^{2024}=0\\ \Rightarrow\left(x-5\right)^{2022}\left[1-\left(x-5\right)^2\right]=0\\ \Rightarrow\left[{}\begin{matrix}\left(x-5\right)^{2022}=0\\1-\left(x-5\right)^2=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x-5=0\\\left(x-5\right)^2=1\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=5\\\left(x-5\right)^2=\left(\pm1\right)^2\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=5\\x=6\\x=4\end{matrix}\right.\)

Answer 2

[『Kuroba ム Tsuki Ryoo ︵²ᵏ⁷』]

`#3107.101107`

\(\left(x-5\right)^{2022}=\left(x-5\right)^{2024}\)

\(\Rightarrow\left(x-5\right)^{2022}-\left(x-5\right)^{2024}=0\\ \Rightarrow\left(x-5\right)^{2022}\cdot\left[1-\left(x-5\right)^2\right]=0\\ \Rightarrow\left[{}\begin{matrix}\left(x-5\right)^{2022}=0\\1-\left(x-5\right)^2=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x-5=0\\\left(x-5\right)^2=1\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=5\\\left(x-5\right)^2=\left(\pm1\right)^2\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=5\\x-5=1\\x-5=-1\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=5\\x=6\\x=4\end{matrix}\right.\)

Vậy, \(x\in\left\{4;5;6\right\}.\)