Đáp án :
`a)n∈ {-10; -2; -1; 7}` thì `n-7 \vdots 2n+3`
`b)n∈{-10; -4; -2; 4}` thì `n^2-2 \vdots n+3`
Giải thích các bước giải :
`a)n-7 \vdots 2n+3`
`=>2(n-7) \vdots 2n+3`
`=>(2n+3)-14-3 \vdots 2n+3`
`=>-17 \vdots 2n+3`
`=>2n+3 ∈ Ư(-17)`
`Ư(-17)={±1; ±17}`
`=>2n+3 ∈ {±1; ±17}`
`=>n∈ {-10; -2; -1; 7}`
Vậy : `n∈ {-10; -2; -1; 7}` thì `n-7 \vdots 2n+3`
`b)n^2-2 \vdots n+3`
`=>(n^2-9)-2+9 \vdots n+3`
`=>(n-3)(n+3)+7 \vdots n+3`
`=>7 \vdots n+3`
`=>n+3 ∈ Ư(7)`
`Ư(7)={±1; ±7}`
`=>n+3∈{±1; ±7}`
`=>n∈{-10; -4; -2; 4}`
Vậy : `n∈{-10; -4; -2; 4}` thì `n^2-2 \vdots n+3`
