Question

\(\dfrac{x}{-3}=\dfrac{y}{-8}vàx^2-y^2=\dfrac{-44}{5}\)

Answer 1

Đặt \(\dfrac{x}{-3}=\dfrac{y}{-8}=k\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=3k\\y=8k\end{matrix}\right.\)

Ta có: \(x^2-y^2=-\dfrac{44}{5}\)

\(\Leftrightarrow9k^2-64k^2=-\dfrac{44}{5}\)

\(\Leftrightarrow k^2=\dfrac{4}{25}\)

Trường hợp 1: \(k=\dfrac{2}{5}\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=3k=\dfrac{6}{5}\\y=8k=\dfrac{16}{5}\end{matrix}\right.\)

Trường hợp 2: \(k=-\dfrac{2}{5}\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=3k=\dfrac{-6}{5}\\y=8k=\dfrac{-16}{5}\end{matrix}\right.\)