\(\dfrac{x}{5}-\dfrac{2}{y}=\dfrac{2}{15}\) ; \(y\ne0\)
Ta có :
\(\dfrac{x}{5}-\frac{2}{y}=\dfrac{2}{15}\)
\(\Rightarrow\dfrac{2}{y}=\dfrac{x}{5}-\dfrac{2}{15}\)
\(\Rightarrow\dfrac{2}{y}=\dfrac{3x}{15}-\dfrac{2}{15}\)
\(\Rightarrow\dfrac{2}{y}=\dfrac{3x-2}{15}\)
\(\Rightarrow2\cdot15=y\cdot\left(3x-2\right)\)
\(\Rightarrow30=y\cdot\left(3x-2\right)\)
\(\Rightarrow y;3x-2\inƯ\left(30\right)=\left\{\pm1;\pm2;\pm3;\pm5;\pm6;\pm10;\pm15;\pm30\right\}\)
Ta có bảng sau :
| 3x-2 | -1 | -30 | 1 | 30 | 2 | 15 | -2 | -15 | 3 | 10 | -3 | -10 | 5 | 6 | -5 | -6 |
| x | 1/3 | -28/3 | 1 | 32/3 | 4/3 | 17/3 | 0 | -13/3 | 5/3 | 4 | -1/3 | -8/3 | 7/3 | 8/3 | -1 | -4/3 |
| y | L | L | 30 | L | L | L | L | L | L | 3 | L | L | L | L | L | L |
Vậy x;y thuộc N* thỏa mãn là : x = 1; y = 30
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