Question

[Dien Giap]

Tìm các số nguyên n biết:

a)\(\left(n+4\right)⋮\left(n-1\right)\)             b)\(\left(n^2+2n-3\right)⋮\left(n+1\right)\)

c)\(\left(3n-1\right)⋮\left(n-2\right)\)           d)\(\left(3n+1\right)⋮\left(2n-1\right)\)

bạn nào trả lời nhanh mik tick đúng cho nhé

Answer 1

[Akai Haruma]

Lời giải:

b/ $n^2+2n-3\vdots n+1$

$\Rightarrow n(n+1)+(n+1)-4\vdots n+1$

$\Rightarrow 4\vdots n+1$

$\Rightarrow n+1\in \left\{\pm 1; \pm 2; \pm 4\right\}$

$\Rightarrow n\in \left\{0; -2; 1; -3; 3; -5\right\}$

c/

$3n-1\vdots n-2$

$\Rightarrow 3(n-2)+5\vdots n-2$

$\Rightarrow 5\vdots n-2$

$\Rightarrow n-2\in \left\{\pm 1; \pm 5\right\}$

$\Rightarrow n\in \left\{3; 1; 7; -3\right\}$

d.

$3n+1\vdots 2n-1$

$\Rightarrow 2(3n+1)\vdots 2n-1$

$\Rightarrow 6n+2\vdots 2n-1$

$\Rightarrow 3(2n-1)+5\vdots 2n-1$

$\Rightarrow 5\vdots 2n-1$

$\Rightarrow 2n-1\in \left\{\pm 1; \pm 5\right\}$

$\Rightarrow n\in \left\{0; 1; 3; -2\right\}$ (thỏa mãn)