\(2x=3y\Rightarrow\dfrac{x}{3}=\dfrac{y}{2}=k\Rightarrow x=3k;y=2k\)
\(xy=54\\ \Rightarrow3k.2k=54\\ \Rightarrow6k^2=54\\ \Rightarrow k^2=9\\ \Rightarrow\left[{}\begin{matrix}k=-3\\k=3\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x=-9\\y=-6\end{matrix}\right.\\\left\{{}\begin{matrix}x=9\\y=6\end{matrix}\right.\end{matrix}\right.\)
Ta co : 2x=3y va xy=54
2x=3y⇒x3=y22x=3y⇒x3=y2
Dat ; x3=y2=kx3=y2=k
x=3k
y=2k
x.y=6k2
54=6k2
k2=9
k = +-3
Voi : k=3 => x=3.3=9 ; y=3.2=6
Voi : k=-3=> x=-3.3=-9;y=-3.2=-6
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