\(\Leftrightarrow\left(3x+xy\right)+\left(2y+6\right)=17+6\)
\(\Leftrightarrow x\left(3+y\right)+2\left(y+3\right)=23\)
\(\left(3+y\right)\left(x+2\right)=23\)
Ma \(23=1\cdot23=23\cdot1=-1\cdot-23=-23\cdot-1\)
Bạn thay vào rồi tìm x,y ná
\(3x+xy+2y=17\)
\(\Rightarrow\) \(x\left(3+y\right)+2y+6=23\)
\(\Rightarrow\) \(x\left(y+3\right)+2\left(y+3\right)=23\)
\(\Rightarrow\) \(\left(x+2\right)\left(y+3\right)=23\)
\(\Rightarrow\) \(x+2;y+3\) là ước của 23
Ta có bảng :
| x + 2 | 1 | 23 | -1 | -23 |
| y + 3 | 23 | 1 | -23 | -1 |
| x | -1 | 21 | -3 | -25 |
| y | 20 | -2 | -26 | -4 |
Vậy \(\left(x,y\right)\in\left\{\left(-1;20\right),\left(21;-2\right),\left(-3;-26\right),\left(-25;-4\right)\right\}\)
Study well ! >_<
