5n + 7 \(⋮\) 3n + 2
\(\Rightarrow\) 3( 5n + 7 )\(⋮\) 3n + 2
5 ( 3n + 2)\(⋮\) 3n + 2
3(5n + 7) - 5(3n + 2) \(⋮\)3n + 2
15n + 21 - 15 n - 10 \(⋮\) 3n + 2
11 \(⋮\) 3n + 2
3n + 2 =\(\left\{1;11\right\}\)
3n = \(\left\{-1;9\right\}\)
n = 9 \(\div\) 3
= 3
Vậy n = 3 thì 5n + 7 \(⋮\) 3n + 2
\(5n+7⋮3n+2\)
\(\Rightarrow3\left(5n+7\right)-5\left(3n+2\right)⋮3n+2\)
\(\Rightarrow15n+21-15n-10⋮3n+2\)
\(\Rightarrow11⋮3n+2\)
\(\Rightarrow3n+2\inƯ\left(11\right)\)
\(\Rightarrow3n+2\in\left\{1;-1;11;-11\right\}\)
\(\Rightarrow3n\in\left\{-1;-3;9;-13\right\}\)
\(\Rightarrow n\in\left\{-1;3\right\}\)
Vậy....
5n + 7 \(⋮3n+2\)
Có 3(5n + 7) \(⋮3n+2\)
Và 5(3n + 2) \(⋮3n+2\)
=> 15n + 7 - 15n - 2 \(⋮3n+2\)
=> 5 \(⋮3n+2\)
=> 3n + 2 \(\inƯ\left(5\right)=\left\{\pm1;\pm5\right\}\)
=> 3n = -1; -3; 3; -7
=> n = -\(\dfrac{1}{3};-1;1;-\dfrac{7}{3}\) (thỏa mãn)
@Selina Moon
