\(3n+5⋮2n+1\)

Mà \(2n+1⋮2n+1\)

\(\Leftrightarrow\hept{\begin{cases}6n+10⋮2n+1\\6n+3⋮2n+1\end{cases}}\)

\(\Leftrightarrow7⋮2n+1\)

\(\Leftrightarrow2n+1\inƯ\left(7\right)\)

\(\Leftrightarrow\orbr{\begin{cases}2n+1=1\\2n+1=7\end{cases}}\) \(\Leftrightarrow\orbr{\begin{cases}n=0\\n=6\end{cases}}\)

Vậy ..

a, 1 hoặc 5

a) vi n chia het cho n nen n+5 chia het cho n khi 5 chia het cho n

do do n thuoc U(5)={1;5}

vay n=1 hoac n=5

xin loi nhe tu tu roi minh giai tiep nhe

Ta có:2n+5=2n+2+3=2(x+1)+3

Để 2n+5 chia hết cho n+1 thì 3 chia hết cho n+1

\(\Rightarrow n+1\inƯ\left(3\right)=\left\{-3,-1,1,3\right\}\)

\(\Rightarrow n\in\left\{-4,-2,0,2\right\}\).Vì n\(\in N\) nên n\(\in\left\{0,2\right\}\) thoả mãn

Vậy............

nhầm là 0 và 2

Ta co:2n+5=2*(n+1)+4

giup minh tra loi nha

Toi quen mat cach  lam roi xin loi nhe

a \(n+2⋮3n+5\)

\(\Rightarrow3\left(n+2\right)⋮3n+5\)

\(\Rightarrow3n+5+1⋮3n+5\)

\(\Rightarrow1⋮3n+5\)

\(\Rightarrow3n+5\in\left\{1,-1\right\}\)

\(\Rightarrow n=-2\)(loại)

c \(3n+7⋮n-2\)

\(\Rightarrow2\left(3n+7\right)⋮n-2\)

\(\Rightarrow6n+14⋮n-2\)

\(\Rightarrow3\left(n-2\right)+20⋮n-2\)

\(\Rightarrow20⋮n-2\)

\(\Rightarrow n-2\in\left\{20,1,10,2,5,4,-20,-1,-10,-2,-5,-4\right\}\)

...(như câu a)

câu b đâu

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

\(\Rightarrow\left(3n-3+5\right)⋮\left(n-1\right)\)

\(\Rightarrow5⋮\left(n-1\right)\)

\(\Rightarrow n-1\inƯ\left(5\right)=\left\{-5;-1;1;5\right\}\)

\(\Rightarrow n\in\left\{-4;0;2;6\right\}\)

n-1 chia hết cho n-1 => 3n-3 chia hết cho n-1

3n+2 chia hết cho n-1

=>(3n+2)-(3n-3) chia hết cho n-1

=>5 chia hết cho n-1

=>n-1 thuộc -5;-1;1;5

TH1: n=-5 => n=-4(loại)

TH2: n=-1 => n=0(TM)

TH3: n=1  => n=2(TM)

TH4: n=5  => n=6(TM)

ta co : 3n + 2 = 3(n-1)+5

Vi 3(n-1)+5 chia het cho n-1

De 3n + 2 chia het cho n-1 suy ra 3(n-1)+ 5 chia het cho n-1

suy ra : 5 chia het cho n-1

suy ra n-1 thuoc U(5)={1;5}

n-1=1

n=1+1=2

n-1 =5

n=5+1=6

vay n = 2 hoac n = 6 thi 3n+2 chia het cho n-1