\(\text{a) }\left(5x+1\right)\left(y-1\right)=4\)
\(\Leftrightarrow5x+1,y-1\inƯ\left(4\right)\)
\(\Leftrightarrow5x+1,y-1\in\left\{\pm1;\pm2;\pm4\right\}\)
Ta có bảng :
| 5x + 1 | 1 | -1 | 2 | -2 | 4 | -4 |
| y - 1 | 1 | -1 | 2 | -2 | 4 | -4 |
| x | 0 | -2/5 | 1/5 | -3/5 | 3/5 | -1 |
| y | 2 | 0 | 3 | -1 | 5 | -3 |
\(\text{b) }5xy-5x+y=5\)
\(\Leftrightarrow\left(5xy+y\right)-5x=5\)
\(\Leftrightarrow y\left(5x+1\right)-\left(5x+1\right)-1=5-1\)
\(\Leftrightarrow y\left(5x+1\right)-\left(5x+1\right)-1=4\)
\(\Leftrightarrow\left(y-1\right).\left(5x+1\right)=4\)
\(\Leftrightarrow y-1,5x+1\inƯ\left(4\right)\)
\(\Leftrightarrow y-1,5x+1\in\left\{\pm1;\pm2;\pm4\right\}\)
Ta có bảng :
| y - 1 | 1 | -1 | 2 | -2 | 4 | -4 |
| 5x + 1 | 1 | -1 | 2 | -2 | 4 | -4 |
| y | 2 | 0 | 3 | -1 | 5 | -3 |
| x | 0 | -2/5 | 1/5 | -3/5 | 3/5 | -1 |
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