a/ \(n+5⋮n-2\)
Mà \(n-2⋮n-2\)
\(\Leftrightarrow7⋮n-2\)
\(\Leftrightarrow n-2\inƯ\left(7\right)\)
\(\Leftrightarrow\left[{}\begin{matrix}n-2=1\\n-2=7\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}n=3\\n=9\end{matrix}\right.\)
Vậy ..
b/ \(2n+3⋮n-3\)
Mà \(n-3⋮n-3\)
\(\Leftrightarrow\left\{{}\begin{matrix}2n+3⋮n-3\\2n-6⋮n-3\end{matrix}\right.\)
\(\Leftrightarrow9⋮n-3\)
\(\Leftrightarrow\left[{}\begin{matrix}n-3=1\\n-3=3\\n-3=9\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}n=4\\n=6\\n=12\end{matrix}\right.\)
Vậy ....
c/ \(2n+3⋮3n-2\)
Mà \(3n-2⋮3n-2\)
\(\Leftrightarrow\left\{{}\begin{matrix}6n+9⋮3n-2\\6n-4⋮3n-2\end{matrix}\right.\)
\(\Leftrightarrow13⋮3n-2\)
\(\Leftrightarrow3n-2\inƯ\left(13\right)\)
\(\Leftrightarrow\left[{}\begin{matrix}3n-2=1\\3n-2=13\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}n=1\\n=5\end{matrix}\right.\)
Vậy ...
d/ \(n^2+2⋮n+1\)
Mà \(n+1⋮n+1\)
\(\Leftrightarrow\left\{{}\begin{matrix}n^2+2⋮n+1\\n^2+1⋮n+1\end{matrix}\right.\)
\(\Leftrightarrow1⋮n+1\)
\(\Leftrightarrow n+1\inƯ\left(1\right)\)
\(\Leftrightarrow n+1=1\)
\(\Leftrightarrow n=0\)
Vậy ..
T ủng hộ cách khác câu d nè:v
\(n^2+2=n^2-1+3=\left(n+1\right)\left(n-1\right)+3=.......\)