Câu hỏi của Long Nguyễn

Question

n2 - 2n - 22 là bội của n + 3

Lightning Farron · Accepted Answer

$n^2-2n-22$ là bội $n+3$

$\Rightarrow n^2-2n-22⋮n+3$

$\Rightarrow n^2+3n-5n-22⋮n+3$

$\Rightarrow n\left(n+3\right)-5n-22⋮n+3$

Ta có: $n\left(n+3\right)⋮n+3$  nên để $n^2-2n-22⋮n+3$

thì $-5n-22⋮n-3$$\Rightarrow-5\left(n-3\right)-7⋮n-3$

Mà $-5\left(n-3\right)⋮n-3$ suy ra $-7⋮n-3$

$\Rightarrow n-3\inƯ\left(-7\right)=\left\{1;-1;7;-7\right\}$

$\Rightarrow n\in\left\{4;2;10;-4\right\}$Câu trả lời: $n^2-2n-22$ là bội $n+3$

$\Rightarrow n^2-2n-22⋮n+3$

$\Rightarrow n^2+3n-5n-22⋮n+3$

$\Rightarrow n\left(n+3\right)-5n-22⋮n+3$

Ta có: $n\left(n+3\right)⋮n+3$  nên để $n^2-2n-22⋮n+3$

thì $-5n-22⋮n-3$$\Rightarrow-5\left(n-3\right)-7⋮n-3$

Mà $-5\left(n-3\right)⋮n-3$ suy ra $-7⋮n-3$

$\Rightarrow n-3\inƯ\left(-7\right)=\left\{1;-1;7;-7\right\}$

$\Rightarrow n\in\left\{4;2;10;-4\right\}$

Hồ Châu Anh · Answer

n2−2n−22 là bội �+3n+3

⇒�2−2�−22⋮�+3⇒n2−2n−22⋮n+3

⇒�2+3�−5�−22⋮�+3⇒n2+3n−5n−22⋮n+3

⇒�(�+3)−5�−22⋮�+3⇒n(n+3)−5n−22⋮n+3

Ta có: �(�+3)⋮�+3n(n+3)⋮n+3 nên để �2−2�−22⋮�+3n2−2n−22⋮n+3

thì −5�−22⋮�−3−5n−22⋮n−3⇒−5(�−3)−7⋮�−3⇒−5(n−3)−7⋮n−3

Mà −5(�−3)⋮�−3−5(n−3)⋮n−3 suy ra −7⋮�−3−7⋮n−3

⇒�−3∈Ư(−7)={1;−1;7;−7}⇒n−3∈Ư(−7)={1;−1;7;−7}

⇒�∈{4;2;10;−4}⇒n∈{4;2;10;−4}Câu trả lời: n2−2n−22 là bội �+3n+3