Question

Tìm số tự nhiên để 7n + 6 chia hết cho 3n - 2

Giải đầy đủ giúp mình với ạ 

Answer 1

\(\Rightarrow\left(21n+18\right)⋮\left(3n-2\right)\\ \Rightarrow\left(21n-14+32\right)⋮\left(3n-2\right)\\ \Rightarrow\left[7n\left(3n-2\right)+32\right]⋮\left(3n-2\right)\\ \Rightarrow3n-2\inƯ\left(32\right)=\left\{1;2;4;8;16;32\right\}\\ \Rightarrow3n\in\left\{3;4;6;10;18;34\right\}\\ \Rightarrow n\in\left\{1;2;6\right\}\left(n\in N\right)\)

Answer 2

\(\Leftrightarrow3n-2\in\left\{1;-1;2;-2;4;-4;8;-8;16;-16;32;-32\right\}\)

hay \(n\in\left\{1;0;2;6\right\}\)

Answer 3

⇒(21n+18)⋮(3n−2)

⇒(21n−14+32)⋮(3n−2)

⇒[7n(3n−2)+32]⋮(3n−2)

⇒3n−2∈Ư(32)={1;2;4;8;16;32}

⇒3n∈{3;4;6;10;18;34}

⇒n∈{1;2;6}(n∈N)