Đặt :
\(\dfrac{x}{2}=\dfrac{y}{3}=\dfrac{z}{5}=k\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=2k\\y=3k\\z=5k\end{matrix}\right.\) \(\left(1\right)\)
Thay \(\left(1\right)\) vào \(xyz=810\) ta dduocj :
\(2k.3k.5k=810\)
\(\Leftrightarrow30k^3=810\)
\(\Leftrightarrow k^3=27\)
\(\Leftrightarrow k=3\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=6\\y=9\\z=15\end{matrix}\right.\)
Vậy ..
Đặt \(\dfrac{x}{2}=\dfrac{y}{3}=\dfrac{z}{5}=k\Leftrightarrow\left\{{}\begin{matrix}x=2k\\y=3k\\z=5k\end{matrix}\right.\)
mà xyz = 810
hay \(2k.3k.5k=810\)
\(\Rightarrow30.k^2=810\)
\(\Rightarrow k^2=27=3^3\)
\(\Rightarrow k=3\)
Với k = 3 \(\Rightarrow\left\{{}\begin{matrix}x=2.3=6\\y=3.3=9\\z=5.3=15\end{matrix}\right.\)
Vậy.........