1,Tìm n \(\in\)Z sao cho 2n-1 \(⋮\)9-n
Tìm \(n\in Z\) sao cho : 2n-3 chia hết cho n+1
ta co: 2n-3 chia het cho n+1
n+1 chia het cho n+1
=>2(n+1) chia het cho n+1
hay 2n+2 chia het cho n+1
=>(2n+2)-(2n-3) chia het cho n-1
5 chia het cho n-1
=> n-1 thuoc uoc cua 5 ={1;5;-1;-5}
=> n thuoc{2;6;0;-4}
Tìm \(n\in Z\)sao cho (3n-4) chia hết cho (2n-1)
\(\left(3n-4\right)⋮\left(2n-1\right)\Rightarrow n\in\left\{3\right\}\)
Tìm n\(\in\)Z sao cho: 2n-1 là bội chung của n+3
a, tìm n thuộc Z để 2n-1 chia hết cho n+1
b, tìm số nguyên n sao cho 2n-1 là bội của n+3
tìm \(n\in Z\)sao cho
2n - 3 \(⋮\)n + 1
\(2n-3⋮n+1\)
\(\Rightarrow\left(2n+2\right)-2-3⋮n+1\)
\(\Rightarrow2\left(n+1\right)-5⋮n+1\)
\(2\left(n+1\right)⋮n+1\)
\(\Rightarrow-5⋮n+1\)
\(\Rightarrow\) \(n+1\inƯ\left(-5\right)\)
đến đây dễ r`, bn tự lm tiếp đi!
\(2n-3⋮n+1\)
\(\Rightarrow2n+2-5⋮n+1\)
mà \(2n+2⋮n+1\)
\(\Rightarrow5⋮n+1\)
\(\Rightarrow n+1\inƯ\left(5\right)\)
\(\Rightarrow n+1\in\left\{1;\left(-1\right);5;\left(-5\right)\right\}\)
\(\Rightarrow n\in\left\{0;\left(-2\right);\left(-6\right);4\right\}\)
vậy :n = 0
n = -2
n = -6
n = 4
2n - 3 \(⋮\)n + 1
=> 2n + 2 - 5 \(⋮\)n + 1
=> 2 ( n + 1 ) - 5 \(⋮\)n + 1
Ta thấy 2 ( n + 1 ) \(⋮\)n + 1
=> 5 \(⋮\)n + 1
=> n + 1 \(\in\)Ư ( 5 )
Ư ( 5 ) = { 1 ; - 1 ; 5 ; - 5 )
Ta có bảng sau :
n + 1 | 1 | - 1 | 5 | - 5 |
n | 0 | - 2 | 4 | - 6 |
Vậy .....
a,Tìm a,b ∈ Z biết A (b+1) =3
b, tìm n ∈ Z sao cho 2n+7 ⋮ n+1
c, tìm x,y ∈ Z sao cho xy + x-y =6
\(\dfrac{help}{me}\)
a) \(a\left(b+1\right)=3\left(a;b\inℤ\right)\)
\(\Rightarrow a;\left(b+1\right)\in U\left(3\right)=\left\{-1;1;-3;3\right\}\)
\(\Rightarrow\left(a;b\right)\in\left\{\left(-1;-4\right);\left(1;2\right);\left(-3;-2\right);\left(3;0\right)\right\}\)
b) \(2n+7⋮n+1\left(n\inℤ\right)\)
\(\Rightarrow2n+7-2\left(n+1\right)⋮n+1\)
\(\Rightarrow2n+7-2n-2⋮n+1\)
\(\Rightarrow5⋮n+1\)
\(\Rightarrow n+1\in U\left(5\right)=\left\{-1;1;-5;5\right\}\)
\(\Rightarrow n\in\left\{-2;0;-6;4\right\}\)
c) \(xy+x-y=6\left(x;y\inℤ\right)\)
\(\Rightarrow x\left(y+1\right)-y-1+1=6\)
\(\Rightarrow x\left(y+1\right)-\left(y+1\right)=5\)
\(\Rightarrow\left(x-1\right)\left(y+1\right)=5\)
\(\Rightarrow\left(x-1\right);\left(y+1\right)\in U\left(5\right)=\left\{-1;1;-5;5\right\}\)
\(\Rightarrow\left(x;y\right)\in\left\{\left(-0;-6\right);\left(2;4\right);\left(-4;-2\right);\left(6;0\right)\right\}\)
Tìm n thuộc Z sao cho 2n - 3 : n + 1
Ta có: \(2n-3⋮n+1\)
\(\Leftrightarrow-5⋮n+1\)
\(\Leftrightarrow n+1\in\left\{1;-1;5;-5\right\}\)
hay \(n\in\left\{0;-2;4;-6\right\}\)
Tìm n thuộc Z sao cho 2n - 3 : n + 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`
Để \(2n-3⋮n+1\)
<=> \(2n-3-2\left(n+1\right)⋮n+1\)
<=> \(-5⋮n+1\)
<=> \(n+1\inƯ\left(5\right)\)
<=> \(n+1\in\left\{-5;-1;1;5\right\}\)
<=> \(n\in\left\{-6;-2;0;4\right\}\)
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 |
Tìm n € Z sao cho 2n - 3 chia hết cho n+1
Tham khảo:
2n-3 chia hết cho n+1
=> 2n+2-5 chia hết cho n+1
=> 2(n+1)-5 chia hết cho n+1
Mà 2(n+1) chia hết cho n+1 => 5 chia hết cho n+1
=> n+1 thuộc Ư(5) ={1;-1;5;-5}
TH1: n+1=1 => n=0 thuộc Z
TH2: n+1=-1 => n=-2 thuộc Z
TH3: n+1=5 => n=4 thuộc Z
TH4: n+1=-5 => n=-6 thuộc Z
=> n thuộc {0;-2;4;6}