Question

\(\dfrac{x}{-2}\)=\(\dfrac{y}{3}\) và x² y²= -45

Answer 1

Sửa đề: \(x^2-y^2=-45\)

Đặt \(\dfrac{x}{-2}=\dfrac{y}{3}=k\)

=>\(\left\{{}\begin{matrix}x=-2k\\y=3k\end{matrix}\right.\)

\(x^2-y^2=-45\)

=>\(\left(-2k\right)^2-\left(3k\right)^2=-45\)

=>\(4k^2-9k^2=-45\)

=>\(-5k^2=-45\)

=>\(k^2=9\)

=>\(\left[{}\begin{matrix}k=3\\k=-3\end{matrix}\right.\)

TH1: k=3

=>\(\left\{{}\begin{matrix}x=-2\cdot3=-6\\y=3\cdot3=9\end{matrix}\right.\)

TH2: k=-3

=>\(\left\{{}\begin{matrix}x=-2\cdot\left(-3\right)=6\\y=3\cdot\left(-3\right)=-9\end{matrix}\right.\)