Ta có: \(\frac{x}{2}=\frac{y}{3}.\)
=> \(\frac{x}{2}=\frac{y}{3}\) và \(x.y=5400.\)
Đặt \(\frac{x}{2}=\frac{y}{3}=k\Rightarrow\left\{{}\begin{matrix}x=2k\\y=3k\end{matrix}\right.\)
Có: \(x.y=5400\)
=> \(2k.3k=5400\)
=> \(6.k^2=5400\)
=> \(k^2=5400:6\)
=> \(k^2=900\)
=> \(k=\pm30.\)
TH1: \(k=30.\)
\(\Rightarrow\left\{{}\begin{matrix}x=2.30=60\\y=3.30=90\end{matrix}\right.\)
TH2: \(k=-30.\)
\(\Rightarrow\left\{{}\begin{matrix}x=2.\left(-30\right)=-60\\x=3.\left(-30\right)=-90\end{matrix}\right.\)
Vậy \(\left(x;y\right)=\left(60;90\right),\left(-60;-90\right).\)
Chúc bạn học tốt!
