Đặt \(\dfrac{x}{3}=\dfrac{y}{7}=k\)
\(\Rightarrow\left\{{}\begin{matrix}x=3k\\y=7k\end{matrix}\right.\)
Mà \(x.y=84\)
\(\Rightarrow3k.7k=84\)
\(\Rightarrow21k^2=84\)
\(\Rightarrow k^2=4\)
\(\Rightarrow k=\pm2\)
+)Nếu \(k=-2\Rightarrow\left\{{}\begin{matrix}x=3.\left(-2\right)=-6\\y=7.\left(-2\right)=-14\end{matrix}\right.\)
+)Nếu \(k=2\Rightarrow\left\{{}\begin{matrix}x=3.2=6\\y=7.2=14\end{matrix}\right.\)
Vậy \(\left(x;y\right)\in\left\{\left(-6;-14\right),\left(6;14\right)\right\}\)
Đặt:
\(\dfrac{x}{3}=\dfrac{y}{7}=t\Leftrightarrow\left\{{}\begin{matrix}x=3t\\y=7t\end{matrix}\right.\)
Hay \(3t.7t=84\Leftrightarrow21t^2=84\Leftrightarrow t^2=4\Leftrightarrow t=\pm2\)
Với \(t=2\) thì \(\left\{{}\begin{matrix}x=2.3=6\\y=2.4=17\end{matrix}\right.\)
Với \(t=-2\) thì \(\left\{{}\begin{matrix}x=-2.3=-6\\y=-2.7=-14\end{matrix}\right.\)
