Question

Các số tự nhiên x thỏa mãn: (x – 2018)^x+1 – (x-2018)^x+11 = 0 là

Answer 1

\(\Leftrightarrow\left(x-2018\right)^{x+1}-\left(x-2018\right)^{x+1}.\left(x-2018\right)^{10}=0\)

\(\Leftrightarrow\left(x-2018\right)^{x+1}\left(1-\left(x-2018\right)^{10}\right)=0\)

\(\Leftrightarrow\left\{{}\begin{matrix}\left(x-2018\right)^{x+1}=0\\1-\left(x-2018\right)^{10}=0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x-2018=0\\\left(x-2018\right)^{10}=1\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=2018\\x=2019\end{matrix}\right.\)