Question

Tìm n thuộc Z sao cho 2n - 3 : n + 1

 

Answer 1

`2n-3 vdots n+1`

`=>2n+2-5 vdots n+1`

`=>2(n+1)-5 vdots n+1`

`=>5 vdots n+1` do `2(n+1) vdots n+1`

`=>n+1 in Ư(5)={+-1,+-5}`

`=>n in {0,-2,4,-6}`

Vậy `n in {0,-2,4,-6}` thì `2n-3 vdots n+1`

Answer 2

Để \(2n-3⋮n+1\)

<=> \(2n-3-2\left(n+1\right)⋮n+1\)

<=> \(-5⋮n+1\)

<=> \(n+1\inƯ\left(5\right)\)

<=> \(n+1\in\left\{-5;-1;1;5\right\}\)

<=> \(n\in\left\{-6;-2;0;4\right\}\)

Answer 3

Giải:

\(2n-3⋮n+1\) 

\(\Rightarrow2n+2-5⋮n+1\) 

\(\Rightarrow5⋮n+1\) 

\(\Rightarrow n+1\inƯ\left(5\right)=\left\{\pm1;\pm5\right\}\) 

Ta có bảng giá trị:

 

n+1	-5	-1	1	5
n	-6	-2	0	4

Vậy \(n\in\left\{-6;-2;0;4\right\}\)