\(\frac{x}{4}=\frac{y}{7}=k\)
\(\Rightarrow\hept{\begin{cases}x=4k\\y=7k\end{cases}}\)
xy = 112
=> 4k . 7k = 112
=> 28 . k2 = 112
=> k2 = 4 \(\Rightarrow\hept{\begin{cases}k=4\\k=-4\end{cases}}\)
=> \(\hept{\begin{cases}k=4\Rightarrow\hept{\begin{cases}x=16\\y=28\end{cases}}\\k=-4\Rightarrow\hept{\begin{cases}x=-16\\y=-28\end{cases}}\end{cases}}\)
Theo đầu bài ta có:
\(\frac{x}{4}=\frac{y}{7}\)
\(\Rightarrow\left(\frac{x}{4}\right)^2=\frac{x}{4}\cdot\frac{y}{7}=\frac{112}{28}=4\)
\(\Rightarrow\frac{x}{4}=\frac{y}{7}=\sqrt{4}=2\)
\(\Rightarrow x=2\cdot4=8\)
\(\Rightarrow y=2\cdot7=14\)
Đặt \(\frac{x}{4}=\frac{y}{7}=k\)
\(\Rightarrow\hept{\begin{cases}x=4k\\y=7k\end{cases}}\)
Thay vào ta có :
\(4k.7k=112\)
\(28.k^2=112\)
\(k^2=4\)
\(k^2=2^2\)hoặc \(\left(-2\right)^2\)
\(k=\pm2\)
+ ) Nếu \(k=2\)\(\Rightarrow\hept{\begin{cases}x=4.2=8\\y=7.2=14\end{cases}}\)
+ ) Nếu \(k=-2\)\(\Rightarrow\hept{\begin{cases}x=4.\left(-2\right)=-8\\y=7.\left(-2\right)=-14\end{cases}}\)