Giải:
Áp dụng tính chất dãy tỉ số bằng nhau ta có:
\(\dfrac{3x-2y}{4}=\dfrac{2z-4x}{3}=\dfrac{4y-3z}{2}=\dfrac{12x-8y}{16}=\dfrac{6z-12x}{9}=\dfrac{8y-6z}{4}\)
\(=\dfrac{12x-8y+6z-12x+8y-6z}{16+9+4}=\dfrac{0}{16+9+4}=0\)
\(\Rightarrow\left\{{}\begin{matrix}\dfrac{12x-8y}{16}=0\\\dfrac{6z-12x}{9}=0\\\dfrac{8y-6z}{4}=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}12x-8y=0\\6z-12x=0\\8y-6z=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}12x=8y\\6z=12x\\8y=6z\end{matrix}\right.\)
\(\Rightarrow12x=8y=6z\)
\(\Rightarrow6x=4y=3z\)
\(\Rightarrow\dfrac{6x}{12}=\dfrac{4y}{12}=\dfrac{3z}{12}\)
\(\Rightarrow\dfrac{x}{2}=\dfrac{y}{3}=\dfrac{z}{4}\)
Vậy x, y, z tỉ lệ với 2, 3, 4
