\(\left(3n-4\right)⋮\left(n+1\right)\\ \Rightarrow\left(3n+3-7\right)⋮\left(n+1\right)\\ \Rightarrow\left[3\left(n+1\right)-7\right]⋮\left(n+1\right)\)
Mà \(3\left(n+1\right)⋮\left(n+1\right)\Rightarrow-7⋮\left(n+1\right)\)
\(\Rightarrow n+1\inƯ\left(-7\right)=\left\{-7;-1;1;7\right\}\\ \Rightarrow n\in\left\{-8;-2;0;6\right\}\)
TL:
Vì \(n+1⋮n+1\)
\(\Rightarrow3\cdot\left(n+1\right)⋮n+1\)
\(\Rightarrow3n+3⋮n+1\)
Mà \(3n-4⋮n+1\)
\(\Rightarrow\left(3n-4\right)-\left(3n+3\right)⋮n+1\)
\(\Rightarrow3n-4-3n-3⋮n+1\)
\(\Rightarrow-7⋮n+1\)
\(\Rightarrow n+1\inƯ\left(-7\right)\)
\(\Rightarrow n+1\in\left\{1;7;-1;-7\right\}\)
\(\Rightarrow n\in\left\{0;6;-2;-8\right\}\)
Thử lại:
| \(3n-4\) | \(-4\) | \(14\) | \(-10\) | \(-28\) |
| \(n+1\) | \(1\) | \(7\) | \(-1\) | \(-7\) |
| Kết luận | \(\left(-4\right)⋮1\) Chọn | \(14⋮7\) Chọn | \(\left(-10\right)⋮\left(-1\right)\) | \(\left(-28\right)⋮\left(-7\right)\) Chọn |
Vậy \(n\in\left\{0;6;-2;-8\right\}\)
CHÚC BẠN HỌC TÔT NHÉ.
