Theo đề ra, ta có: \(\frac{x}{3}=\frac{y}{7}\)
Đặt \(\frac{x}{3}=\frac{y}{7}=k\)
=> \(\left\{\begin{matrix}x=3k\\y=7k\end{matrix}\right.\)
Lại có: \(x.y=336\)
\(\Leftrightarrow3k.7k=336\)
\(\Leftrightarrow\left[\begin{matrix}k=4\\k=-4\end{matrix}\right.\)
+ Nếu k = 4
=> \(\left\{\begin{matrix}x=12\\y=28\end{matrix}\right.\)
=> \(x^2+y^2=12^2+28^2=928\)
+ Nếu k = - 4
=> \(\left\{\begin{matrix}x=-12\\y=-28\end{matrix}\right.\)
=> \(x^2+y^2=\left(-12\right)^2+\left(-28\right)^2=928\)
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