Lời giải:
$2x=3y\Leftrightarrow \frac{x}{3}=\frac{y}{2}\Leftrightarrow \frac{x}{6}=\frac{y}{4}$
$5y=4z\Leftrightarrow \frac{y}{4}=\frac{z}{5}$
Vậy:
$\frac{x}{6}=\frac{y}{4}=\frac{z}{5}$
$\Rightarrow (\frac{x}{6})^3=(\frac{y}{4})^3=(\frac{z}{5})^3=\frac{xyz}{6.4.5}=\frac{120}{120}=1$
$\Rightarrow \frac{x}{6}=\frac{y}{4}=\frac{z}{5}=1$
$\Rightarrow x=6; y=4; z=5$
Ta có: 2x=3y
nên \(\dfrac{x}{3}=\dfrac{y}{2}\)
hay \(\dfrac{x}{6}=\dfrac{y}{4}\)(1)
Ta có: 5y=4z
nên \(\dfrac{y}{4}=\dfrac{z}{5}\)(2)
Từ (1) và (2) suy ra \(\dfrac{x}{6}=\dfrac{y}{4}=\dfrac{z}{5}\)
Đặt \(\dfrac{x}{6}=\dfrac{y}{4}=\dfrac{z}{5}=k\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=6k\\y=4k\\z=5k\end{matrix}\right.\)
Ta có: xyz=120
nên \(120k^3=120\)
\(\Leftrightarrow k^3=1\)
hay k=1
Suy ra: x=6; y=4; z=5
