\(\left(x-2\right)^{x+2}=\left(x-2\right)^{x+4}\)
\(\Leftrightarrow\left(x-2\right)^{x+2}-\left(x-2\right)^{x+4}=0\)
\(\Leftrightarrow\left(x-2\right)^{x+2}.\left[1+\left(x-2\right)^2\right]=0\)
\(\Rightarrow\orbr{\begin{cases}\left(x-2\right)^{x+2}=0\\1+\left(x-2\right)^2=0\end{cases}\Rightarrow\orbr{\begin{cases}x-2=0\\x+2=1\end{cases}\Rightarrow}\orbr{\begin{cases}x=2\\x=-1\end{cases}}}\)
Vậy x=2 hoặc x=-1
\(\left(x-2\right)^{x+2}=\left(x-2\right)^{x+4}\)
\(\left(x-2\right)^{x+2}=\left(x-2\right)^{x+2}.\left(x-2\right)^2\)
\(\Rightarrow\left(x-2\right)^2=1\)
\(\Rightarrow\hept{\begin{cases}x-2=1\\x-2=-1\end{cases}\Rightarrow\hept{\begin{cases}x=3\\x=1\end{cases}}}\)
nhầm
\(\orbr{\begin{cases}x-2=1\\x+2=0\end{cases}\Rightarrow\orbr{\begin{cases}x=3\\x=-2\end{cases}}}\)
