\(12x=-15y=10z\)
\(\Rightarrow\dfrac{12x}{60}=\dfrac{-15y}{60}=\dfrac{10z}{60}\)
\(\Rightarrow\dfrac{x}{5}=\dfrac{y}{-4}=\dfrac{z}{6}\)
Đặt: \(\dfrac{x}{5}=\dfrac{y}{-4}=\dfrac{z}{6}=k\)
\(\Rightarrow x=5k;y=-4k;z=6k\)
Ta có: \(xyz=120\)
\(\Rightarrow5k\cdot-4k\cdot6k=120\)
\(\Rightarrow-120k^3=120\)
\(\Rightarrow k^3=-1\)
\(\Rightarrow k=-1\)
\(\Rightarrow\left\{{}\begin{matrix}\dfrac{x}{5}=-1\\\dfrac{y}{-4}=-1\\\dfrac{z}{6}=-1\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x=-1\cdot5=-5\\y=-4\cdot-1=4\\z=-1\cdot6=-6\end{matrix}\right.\)
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