\(\left(x-5\right)^{x+3}-\left(x-5\right)^{x+13}=0\)
\(\Leftrightarrow\left(x-5\right)^{x+3}.\left[1-\left(x-5\right)^{x+10}\right]=0\)
\(\Leftrightarrow\left[{}\begin{matrix}\left(x-5\right)^{x+3}=0\\1-\left(x-5\right)^{x+10}=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x-5=0\\\left(x-5\right)^{x+10}=1\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x-5=0\\x-5=1\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=5\\x=6\end{matrix}\right.\)
Vậy..
\(\left(x-5\right)^{x+3}-\left(x-5\right)^{x+13}=0\)
\(\Rightarrow\left(x-5\right)^{x+3}.\left[1-\left(x-5\right)^{x+10}\right]=0\)
\(\Rightarrow\left[{}\begin{matrix}\left(x-5\right)^{x+3}=0\\1-\left(x-5\right)^{x+10}=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x-5=0\\\left(x-5\right)^{x+10}=1\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=5\\x-5=1\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=5\\x=6\end{matrix}\right.\)
Vậy \(x\in\left\{5;6\right\}.\)
Chúc bạn học tốt!
