a/ \(n^2+2n+7⋮n+2\)
Mà \(n+2⋮n+2\)
\(\Leftrightarrow\left\{{}\begin{matrix}n^2+2n+7⋮n+2\\n^2+2n⋮n+2\end{matrix}\right.\)
\(\Leftrightarrow7⋮n+2\)
\(\Leftrightarrow n+2\inƯ\left(7\right)\)
\(\Leftrightarrow\left[{}\begin{matrix}n+2=1\\n+2=7\\n+2=-1\\n+2=-7\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}n=-1\\n=5\\n=-3\\n=-9\end{matrix}\right.\)
Vậy ....
b/ \(n^2+1⋮n-1\)
Mà \(n-1⋮n-1\)
\(\Leftrightarrow\left\{{}\begin{matrix}n^2+1⋮n-1\\n^2-1⋮n-1\end{matrix}\right.\)
\(\Leftrightarrow2⋮n-1\)
\(\Leftrightarrow n-1\inƯ\left(2\right)\)
\(\Leftrightarrow\left[{}\begin{matrix}n-1=1\\n-1=2\\n-1=-1\\n-1=-2\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}n=2\\n=3\\n=0\\n=-1\end{matrix}\right.\)
Vậy ....
\(n^2+1⋮n-1\)
Mà \(n-1⋮n-1\)
\(\Leftrightarrow\left\{{}\begin{matrix}n^2+1⋮n-1\\n^2-n⋮n-1\end{matrix}\right.\)
\(\Leftrightarrow n+1⋮n-1\)
Mà \(n-1⋮n-1\)
\(\Leftrightarrow2⋮n-1\)
\(\Leftrightarrow n-1\inƯ\left(2\right)\)
\(\Leftrightarrow\left[{}\begin{matrix}n-1=1\\n-1=2\\n-1=-1\\n-1=-2\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}n=2\\n=3\\n=0\\n=-1\end{matrix}\right.\)
Vậy ...
