Question

Tìm số TN n để :

a) (n + 3) \(⋮\) (n - 2)

b) (2n + 9) \(⋮\) (n + 1)

Answer 1

a) (n + 3) ⋮ (n - 2)

b) (2n + 9) ⋮ (n + 1)

Bài làm

a) (n + 3) ⋮ (n - 2)

ta có \((n+3)-(n-2)\)

\((n-2)⋮(n-2)\)

\(\Rightarrow[(n+3)-(n-2)]\) \(⋮\) \((n-2)\)

\(\Rightarrow\) 5 \(⋮\) (n - 2 )

\(\Leftrightarrow\) (n - 2) \(\in\) Ư₍₅₎ = \(\left\{1;5\right\}\)

Nếu n - 2 = 1 \(\Rightarrow\) n = 3

Nếu n - 2 = 5 \(\Rightarrow\) n = 7

Vậy n = \(\left\{3;7\right\}\) Thì (n + 3 ) \(⋮\) (n - 3 )