\(\left(x-5\right)^4=\left(x-5\right)\)
\(\Leftrightarrow\left(x-5\right)^4-\left(x-5\right)=0\)
\(\Leftrightarrow\left[\left(x-5\right)^3-1\right]\left(x-5\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}\left(x-5\right)^3-1=0\\x-5=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left(x-5\right)^3=1\\x=5\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x-5=1\\x=5\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=6\\x=5\end{matrix}\right.\)
Vậy ............
( x - 5 )4 = ( x - 5 )
- Nếu x - 5 = 0 thì x = 5 mà (5 - 5)4 = (5 - 5). (chọn)
- Nếu x - 5 = 1 thì x = 6 mà (6 - 5)4 = (6 - 5). (chọn)
- Nếu x - 5 = a \(\ge\) 2 thì (x - 5)4 = (x - 5). (vô lý)
Vậy x \(\in\) {5; 6}.
