Question

5x=6y, x.y=120

tìm x và y

gấp nha mn

Answer 1

Ta có: 5x=6y

nên \(\dfrac{x}{6}=\dfrac{y}{5}\)

Đặt \(\dfrac{x}{6}=\dfrac{y}{5}=k\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=6k\\y=5k\end{matrix}\right.\)

Ta có: xy=120

\(\Leftrightarrow30k^2=120\)

\(\Leftrightarrow k^2=4\)

Trường hợp 1: k=2

\(\Leftrightarrow\left\{{}\begin{matrix}x=6k=12\\y=5k=10\end{matrix}\right.\)

Trường hợp 2: k=-2

\(\Leftrightarrow\left\{{}\begin{matrix}x=6k=-12\\y=5k=-10\end{matrix}\right.\)