Question

Tìm số tự nhiên n biết: (2n+1)⋮(6-n)

Answer 1

\(\Rightarrow2n-12+13⋮6-n\)

\(\Rightarrow13⋮6-n\Rightarrow6-n\in\left\{\pm1;\pm13\right\}\)

\(\Rightarrow n\in\left\{19;7;5;-7\right\}\)

Answer 2

(2n+1)\(⋮\)(6-n)

Ta có :

(6-n)\(⋮\)(6-n)

=> 2(6-n)\(⋮\)(6-n)

Hay 12- 2n \(⋮\)(6-n)

=> (12-2n)-(2n+1)\(⋮\)6-n

11\(⋮\)6-n

=> 6-n\(\in\){ 11;-11}

=> n\(\in\) {-5;17}

Answer 3

\(\left(2n+1\right)⋮\left(6-n\right)\)

Ta có : \(\left(6-n\right)⋮\left(6-n\right)\)

=> \(2\left(6-n\right)⋮6-n\)

hay \(12-2n⋮6-n\)

=> \(\left(12-2n\right)-\left(2n+1\right)⋮6-n\)

\(11⋮6-n\)

=>\(6-n\in\left\{11;-11\right\}\)

=>\(n\in\left\{-5;17\right\}\)