Câu hỏi của Alayna

Question

Cho

( n ≠ -1). Tìm  n ∈ N để A  nguyên.

Alone · Accepted Answer

$A=\dfrac{5n+1}{n+1}=\dfrac{5\left(n+1\right)-4}{n+1}$

$Để$ $\dfrac{5n+1}{n+1}\in Z\Rightarrow4⋮n+1$

$\Rightarrow n+1\inƯ\left(4\right)=\left\{-1;-2;-4;1;2;4\right\}$

$n+1=-1\Rightarrow n=-2$

$n+1=-2\Rightarrow n=-3$

$n+1=-4\Rightarrow n=-5$

$n+1=1\Rightarrow n=0$

$n+1=2\Rightarrow n=1$

$n+1=4\Rightarrow n=3$Câu trả lời: $A=\dfrac{5n+1}{n+1}=\dfrac{5\left(n+1\right)-4}{n+1}$

$Để$ $\dfrac{5n+1}{n+1}\in Z\Rightarrow4⋮n+1$

$\Rightarrow n+1\inƯ\left(4\right)=\left\{-1;-2;-4;1;2;4\right\}$

$n+1=-1\Rightarrow n=-2$

$n+1=-2\Rightarrow n=-3$

$n+1=-4\Rightarrow n=-5$

$n+1=1\Rightarrow n=0$

$n+1=2\Rightarrow n=1$

$n+1=4\Rightarrow n=3$

qwerty · Answer

0;1;3Câu trả lời: 0;1;3

Lê Mỹ Linh · Answer

Gía trị A nguyên khi 5n + 1 chia hết cho n + 1

=> 5n + 5 - 4 chia hết cho n + 1

=> 5(n + 1) - 4 chia hết cho n + 1

=> -4 chia hết cho n + 1

=> n + 1 $\in$ Ư(-4) = {$\pm$ 1; $\pm$ 2; $\pm$ 4}

=> n $\in$ {0; -2; 1; -3; 3; -5}

Theo đề bài, có n $\in$ N .

Vậy, n $\in$ {0; 1; 3}Câu trả lời: Gía trị A nguyên khi 5n + 1 chia hết cho n + 1