Tìm a,b ∈ Z biết : ab + 2a + 2b = -17

Đáp án:

Giải thích các bước giải:

`ab + 2a + 2b = -17`

`=> a ( 2 + b ) + 2b = -17`

`=> a ( 2 + b ) + 2b + 4 = -13`

`=> a ( 2 + b ) + 2 ( 2 + b ) = -13`

`=> ( a + 2 ) ( 2 + b ) = -13`

`=> a + 2; 2 + b \in Ư(-13) = { -13; -1; 1; 13 }`

Ta có bảng:

$\begin{array}{|c|c|c|}\hline \text{a + 2}&\text{-13}&\text{-1}&\text{1}&\text{13}\\\hline \text{2 + b}&\text{1}&\text{13}&\text{-13}&\text{-1}\\\hline \text{a}&\text{-15}&\text{-3}&\text{-1}&\text{11}\\\hline \text{b}&\text{-1}&\text{11}&\text{-15}&\text{-3}\\\hline\end{array}$

Vậy ...

`#Sad`