Ta có :
\(n^2+5⋮n+1\)
Mà \(n+1⋮n+1\)
\(\Leftrightarrow\left\{{}\begin{matrix}n^2+5⋮n+1\\n^2+n⋮n+1\end{matrix}\right.\)
\(\Leftrightarrow-n+5⋮n+1\)
Mà \(n+1⋮n+1\)
\(\Leftrightarrow6⋮n+1\)
\(\Leftrightarrow n+1\inƯ\left(6\right)\)
\(\Leftrightarrow\left[{}\begin{matrix}n+1=1\\n+1=2\\n+1=3\\n+1=6\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}n=0\\n=1\\n=2\\n=5\end{matrix}\right.\)
Vậy ..
Theo đề bài ta có:
( n2 + 5 ) \(⋮\)( n + 1 )
\(\Rightarrow\) ( n + 1 )(n+1) + 3 \(⋮\) ( n + 1 )
Mà ( n+1)(n+1 ) \(⋮\) ( n + 1 )
\(\Rightarrow\) 3 \(⋮\) ( n + 1 )
\(\Rightarrow\) n + 1 \(\in\) Ư ( 3 ) = \(\left\{1;3\right\}\)
\(\Rightarrow\)n \(\in\) \(\left\{0;2\right\}\)
Vậy n \(\in\) \(\left\{0;2\right\}\)
Ta có :
n2+5⋮n+1n2+5⋮n+1
Mà n+1⋮n+1n+1⋮n+1
⇔⎧⎨⎩n2+5⋮n+1n2+n⋮n+1⇔{n2+5⋮n+1n2+n⋮n+1
⇔−n+5⋮n+1⇔−n+5⋮n+1
Mà n+1⋮n+1n+1⋮n+1
⇔6⋮n+1⇔6⋮n+1
⇔n+1∈Ư(6)⇔n+1∈Ư(6)
⇔⎡⎢ ⎢ ⎢⎣n+1=1n+1=2n+1=3n+1=6⇔[n+1=1n+1=2n+1=3n+1=6 ⇔⎡⎢ ⎢ ⎢⎣n=0n=1n=2n=5⇔[n=0n=1n=2n=5
Vậy .......
