Tìm n biết
a; 3n +19 chia hết cho n+1
B; 2n+7 chia hết cho n+2
c; 6n+39 chia hết cho 2n+1
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16 tháng 11 2022
1: =>3n-12+17 chia hết cho n-4
=>\(n-4\in\left\{1;-1;17;-17\right\}\)
hay \(n\in\left\{5;3;21;-13\right\}\)
2: =>6n-2+9 chia hết cho 3n-1
=>\(3n-1\in\left\{1;-1;3;-3;9;-9\right\}\)
hay \(n\in\left\{\dfrac{2}{3};0;\dfrac{4}{3};-\dfrac{2}{3};\dfrac{10}{3};-\dfrac{8}{3}\right\}\)
4: =>2n+4-11 chia hết cho n+2
=>\(n+2\in\left\{1;-1;11;-11\right\}\)
hay \(n\in\left\{-1;-3;9;-13\right\}\)
5: =>3n-4 chia hết cho n-3
=>3n-9+5 chia hết cho n-3
=>\(n-3\in\left\{1;-1;5;-5\right\}\)
hay \(n\in\left\{4;2;8;-2\right\}\)
6: =>2n+2-7 chia hết cho n+1
=>\(n+1\in\left\{1;-1;7;-7\right\}\)
hay \(n\in\left\{0;-2;6;-8\right\}\)
A
8 tháng 8 2023
a, Ta có : \(\text{n + 5 = (n - 1)+6}\)
Vì \(\text{(n-1) ⋮ n-1}\)
Nên để \(\text{n+5 ⋮ n-1}\)⋮ `n-1`
Thì \(\text{6 ⋮ n-1}\)
\(\Rightarrow\) \(\text{n - 1 ∈ Ư(6)}\)
\(\Rightarrow\) \(\text{n - 1 ∈}\) \(\left\{\text{±1;±2;±3;±6}\right\}\)
\(\Rightarrow\) \(\text{n ∈}\) \(\left\{\text{0;-1;-2;-5;2;3;4;7}\right\}\) \(\text{( TM )}\)
\(\text{________________________________________________________}\)
b, Ta có : \(\text{2n-4 = (2n+4)- 8 = 2(n+2) - 8}\)
Vì \(\text{2(n+2) ⋮ n+2}\)
Nên để \(\text{2n-4 ⋮ n+2}\)
Thì \(\text{8 ⋮ n+2}\)
\(\Rightarrow\) \(\text{n + 2 ∈ Ư(8)}\)
\(\Rightarrow\) \(\text{n + 2 ∈}\) \(\left\{\text{±1;±2;±4;±8}\right\}\)
\(\Rightarrow\) \(\text{n ∈}\) \(\left\{\text{-3;-4;-6;-10;-1;0;2;6}\right\}\) ( TM )
\(\text{_________________________________________________________________ }\)
c, Ta có :\(\text{ 6n + 4 = (6n + 3) +1 = 3(2n+1) + 1}\)
Vì \(\text{3(2n+1) ⋮ 2n+1}\)
Nên để\(\text{ 6n+4 ⋮ 2n+1}\)
Thì \(\text{1 ⋮ 2n+1}\)
\(\Rightarrow\) \(\text{2n + 1 ∈ Ư(1)}\)
\(\Rightarrow\) \(\text{2n + 1 ∈}\) \(\left\{\text{±1}\right\}\)
\(\Rightarrow\) \(\text{2n ∈}\) \(\left\{\text{-2;0}\right\}\)
\(\Rightarrow\) \(\text{n ∈}\) \(\left\{\text{-1;0}\right\}\) ( TM )
\(\text{_______________________________________}\)
Ta có : \(\text{3 - 2n = -( 2n - 3 ) = -( 2n + 2 ) + 5 = -2( n+1)+5}\)
Vì \(\text{-2(n+1) ⋮ n+1}\)
Nên để \(\text{3-2n ⋮ n+1}\)
Thì\(\text{ 5 ⋮ n + 1}\)
\(\Rightarrow\) \(\text{n + 1 ∈}\) \(\left\{\text{±1;±5}\right\}\)
\(\Rightarrow\) \(\text{n ∈}\) \(\text{-2;-6;0;4}\) ( TM )
HT
15 tháng 7 2015
Đễ nhưng quá nhiều không đủ kiên nhẫn để làm. Bạn đăng lần lượt thôi.
6 tháng 10 2017
n+ 9 \(⋮n-2\)
mà n - 2 \(⋮n-2\)
= n -2 +11 \(⋮n-2\)
=> 11 \(⋮n-2\)
n -2 \(\inư\left(11\right)\in1,11\)
Ta có bảng:
| n-2 | 1 | 11 |
| n | 3 | 13 |
Vậy x = 3; 13
2 tháng 2 2019
\(a)n+7⋮n+2\)
\(\Rightarrow n+2+5⋮n+2\)
Mà n + 2 chia hết cho n + 2 => \(5⋮n+2\)=> n + 2 thuộc Ư\((5)\)\(=\left\{\pm1;\pm5\right\}\)
Lập bảng :
| n + 2 | 1 | -1 | 5 | -5 |
| n | -1 | -3 | 3 | -7 |
Vậy : ...
a) \(3n+19⋮n+1\)
\(\Rightarrow\)\(3\left(n+1\right)+16⋮n+1\)
mà \(3\left(n+1\right)⋮n+1\)\(\Rightarrow\)\(16⋮n+1\)
\(\Rightarrow\)\(n+1\in\left\{1,-1,2,-2,4,-4,8,-8,16,-16\right\}\)
\(\Rightarrow n\in\left\{0,-2,1,-3,3,-5,7,-9,15,-17\right\}\)
b) \(2n+7⋮n+2\)
\(\Rightarrow2\left(n+2\right)+3⋮n+2\)
mà \(2\left(n+2\right)⋮n+2\Rightarrow3⋮n+2\)
\(\Rightarrow n+2\in\left\{1,3,-1,-3\right\}\)
\(\Rightarrow n\in\left\{-1,1,-3,-5\right\}\)
c)\(6n+39⋮2n+1\Rightarrow3\left(2n+1\right)+36⋮2n+1\)
mà\(3\left(2n+1\right)⋮2n+1\)\(\Rightarrow36⋮2n+1\)
\(\Rightarrow2n+1\in\left\{1,-1,2,-2,3,-3,4,-4,6,-6,9,-9,12,-12,18,-18,36,-36\right\}\)
\(\Rightarrow2n\in\left\{0,-2,1,-3,2,-4,3,-5,5,-7,8,-10,11,-13,17,-19,35,-37\right\}\)
\(\Rightarrow\)\(n\in\left\{0,-1,1,-2,4,-5\right\}\)