Question

x/4 = y/5 và xy = 80

Answer 1

Đặt \(\dfrac{x}{4}=\dfrac{y}{5}=k\Leftrightarrow x=4k;y=5k\)

\(xy=80\Leftrightarrow20k^2=80\Leftrightarrow k^2=4\\ \Leftrightarrow\left[{}\begin{matrix}k=2\\k=-2\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=8;y=10\\x=-8;y=-10\end{matrix}\right.\)

Answer 2

\(\dfrac{x}{4}=\dfrac{y}{5}=k\Rightarrow x=4k,y=5k\)

\(xy=80\Rightarrow4k.5k=80\\ \Rightarrow k^2=4\\ \Rightarrow\left[{}\begin{matrix}k=-2\\k=2\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x=-8\\y=-10\end{matrix}\right.\\\left\{{}\begin{matrix}x=8\\y=10\end{matrix}\right.\end{matrix}\right.\)

Vậy \(\left(x,y\right)\in\left\{\left(-8;-10\right);\left(8;10\right)\right\}\)