(x - 2013)x+1 - (x - 2013)x+10 = 0
=> (x - 2013)x+1 = (x - 2013)x+10 (1)
Mà 2 vế có x - 2013 chung (2)
=> x + 1 = x + 10
=> x - x = 10 - 1
=> 0 = 9 (vô lí)
=> x không tồn tại
Bạn kia giải sai rồi
Giải:
Ta có:
\(\left(x-2013\right)^{x+1}-\left(x-2013\right)^{x+10}=0\)
\(\Leftrightarrow\left(x-2013\right)^{x+1}\left[1-\left(x-2013\right)^9\right]=0\)
\(\Leftrightarrow\left[{}\begin{matrix}\left(x-2013\right)^{x+1}=0\\1-\left(x-2013\right)^9=0\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x-2013=0\\\left(x-2013\right)^9=1\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x=2013\\x=2014\end{matrix}\right.\)
Vậy \(\left[{}\begin{matrix}x=2013\\x=2014\end{matrix}\right.\)
