Ta có: \(xy+3x-2y=11\)
\(\Rightarrow xy-2y+3x-6=5\)
\(\Rightarrow y\left(x-2\right)+3\left(x-2\right)=5\)
\(\Rightarrow\left(y+3\right)\left(x-2\right)=5\)
\(\Rightarrow y+3\inƯ\left(5\right);x-2\inƯ\left(5\right)\)
mà \(Ư\left(5\right)=\left\{\pm1;\pm5\right\}\)
\(\Rightarrow y+3\in\left\{\pm1;\pm5\right\}\)
và \(x-2\in\left\{\pm1;\pm5\right\}\)
| \(y+3\) | 1 | \(-1\) | 5 | \(-5\) |
| \(x-2\) | 5 | \(-5\) | 1 | \(-1\) |
| \(x\) | 7 | \(-3\) | 3 | \(1\) |
| \(y\) | \(-2\) | \(-4\) | 2 | \(-8\) |
Vậy ta tìm được các cặp số sau:
\(\left(x,y\right)\) \(\in\left\{\left(7,-2\right);\left(-3,-4\right);\left(3,2\right);\left(1,-8\right)\right\}\)
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