Ta có:
\(\frac{15}{x-9}=\frac{20}{y-12}=\frac{40}{z-24}\)
\(\Rightarrow\frac{x-9}{15}=\frac{y-12}{20}=\frac{z-24}{40}\)
\(\Rightarrow\frac{x}{15}-\frac{3}{5}=\frac{y}{20}-\frac{3}{5}=\frac{z}{40}-\frac{3}{5}\)
\(\Rightarrow\frac{x}{15}=\frac{y}{20}=\frac{z}{40}=k\)
\(\Rightarrow\left\{{}\begin{matrix}x=15k\\y=20k\\z=40k\end{matrix}\right.\)
\(\Rightarrow xy=15k20k=300k^2=1200\)
\(\Rightarrow k^2=4\Rightarrow\left[{}\begin{matrix}k=2\\k=-2\end{matrix}\right.\)
TH1:\(k=2\)
\(\Rightarrow\left\{{}\begin{matrix}x=15k=30\\y=20k=40\\z=40k=80\end{matrix}\right.\)
TH2:\(k=-2\)
\(\Rightarrow\left\{{}\begin{matrix}x=15k=-30\\y=20k=-40\\z=40k=-80\end{matrix}\right.\)