Question

Tìm \(x,y\in\)N* để:

\(\frac{x}{10}-\frac{1}{y}=\frac{3}{10}\)

Answer 1

Ta có: \(\frac{x}{10}-\frac{1}{y}=\frac{3}{10}\)

\(\Rightarrow\frac{1}{y}=\frac{x}{10}-\frac{3}{10}\)

\(\Rightarrow\frac{1}{y}=\frac{x-3}{10}\)

\(\Rightarrow y=\frac{10}{x-3}\)
 Vì   \(y=\frac{10}{x-3}\)\(\Rightarrow\)\(x-3\in U(10)\)\(\Rightarrow x-3\in\left\{\pm1,\pm2\pm5\pm10\right\}\)\(\Rightarrow x\in\left\{4,2,5,1,8,-2,13,-7\right\}\)\(\Rightarrow y\in\left\{\pm10,\pm5,\pm2\pm1\right\}\)

Vậy  \(x\in\left\{4,2,5,1,8,-2,13,-7\right\}\) ,   \(y\in\left\{\pm10,\pm5,\pm2\pm1\right\}\)