Ta có: \(\frac{40}{x-30}=\frac{20}{y-15}=\frac{28}{z-21}.\)
\(\Rightarrow\frac{x-30}{40}=\frac{y-15}{20}=\frac{z-21}{28}.\)
\(\Rightarrow\frac{x}{40}-\frac{3}{4}=\frac{y}{20}-\frac{3}{4}=\frac{z}{28}-\frac{3}{4}\)
\(\Rightarrow\frac{x}{40}=\frac{y}{20}=\frac{z}{28}\) và \(x.y.z=22400.\)
Đặt \(\frac{x}{40}=\frac{y}{20}=\frac{z}{28}=k\Rightarrow\left\{{}\begin{matrix}x=40k\\y=20k\\z=28k\end{matrix}\right.\)
Có: \(x.y.z=22400\)
=> \(40k.20k.28k=22400\)
=> \(22400.k^3=22400\)
=> \(k^3=22400:22400\)
=> \(k^3=1\)
=> \(k=1.\)
Với \(k=1.\)
\(\Rightarrow\left\{{}\begin{matrix}x=40.1=40\\y=20.1=20\\z=28.1=28\end{matrix}\right.\)
Vậy \(\left(x;y;z\right)=\left(40;20;28\right).\)
Chúc bạn học tốt!