Tìm số nguyên x biết : 3x + 4 chia hết cho x - 3

2 câu trả lời

`3x + 4 \vdots x - 3`

`x - 3 \vdots x - 3`

`=> [(3x + 4) - 3(x - 3)] \vdots x - 3`

`=> [(3x + 4) - (3x - 9)] \vdots x - 3`

`=> 13 \vdots x - 3`

`=> x - 3 in Ư(13) = {1; -1; 13; -13}`

`=> x - 3 in {1; -1; 13; -13}`

`=> x in {4; 2; 16; -10} `

Vậy `x in {4; 2; 16; -10} `

 

Ta có: `3x + 4` $\vdots$ `x - 3`

Mà `x - 3` $\vdots$ `x - 3`

`=> (3x + 4) - (x - 3)`$\vdots$ `x - 3`

`=> (3x + 4) - (3x - 9)`$\vdots$ `x - 3`

`=> 3x + 4 - 3x + 9`$\vdots$ `x - 3`

`=> 13` $\vdots$ `x - 3`

`=> x - 3 là Ư(13)`

Ta có bảng sau:

\begin{array}{|c|c|c|}\hline \text{x-3}&\text{1}&\text{-1}&\text{13}&\text{-13}\\\hline \text{x}&\text{4}&\text{2}&\text{16}&\text{-10}\\\hline\end{array}

Vậy `x ∈ { 4; 2; 16; -10 }`