\(\left(x-2\right)^{2x+3}=\left(x-2\right)^{2x+1}\)
\(\Leftrightarrow2x+3=2x+1\)
\(\Leftrightarrow2x-2x=1-3\)
\(\Leftrightarrow2x-2x=-2\) (vô lí)
Vậy .....
\(\left(x-2\right)^{2x+3}=\left(x-2\right)^{2x+1}\) \(\Leftrightarrow\left(x-2\right)^{2x+3}-\left(x-2\right)^{2x+1}=0\)
\(\Leftrightarrow\left(x-2\right)^{2x+1}.\left(\left(x-2\right)^2-1\right)=0\) \(\Leftrightarrow\left[{}\begin{matrix}\left(x-2\right)^{2x+1}=0\\\left(x-2\right)^2-1=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x-2=0\\x^2-4x+4-1=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=2\\x^2-4x+3=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=2\\x^2-3x-x+3=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=2\\x\left(x-3\right)-\left(x-3\right)=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=2\\\left(x-1\right)\left(x-3\right)=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=2\\\left[{}\begin{matrix}x-1=0\\x-3=0\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=2\\\left[{}\begin{matrix}x=1\\x=3\end{matrix}\right.\end{matrix}\right.\) vậy \(x=2;x=1;x=3\)
