Ta có: \(\dfrac{5}{x}=\dfrac{1}{6}+\dfrac{y}{3}\)
\(\Leftrightarrow\dfrac{5}{x}=\dfrac{6y+3}{18}\)
\(\Leftrightarrow3x\left(2y+1\right)=90\)
\(\Leftrightarrow x\left(2y+1\right)=30\)
Vì x,y ∈ N ⇒ x ; 2y+1∈ N
Do 2y+1 là số lẻ:2y+1 ≥ 3
Xét các trường hợp sau:
TH1: \(\left\{{}\begin{matrix}x=2\\2y+1=15\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=2\\y=7\end{matrix}\right.\)
TH2: \(\left\{{}\begin{matrix}x=6\\2y+1=5\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=6\\y=2\end{matrix}\right.\)
TH3: \(\left\{{}\begin{matrix}x=10\\2y+1=3\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=10\\y=0\end{matrix}\right.\)
Vậy(x;y)∈\(\left\{\left(2;7\right);\left(6;2\right);\left(10;0\right)\right\}\)
