\(12x=15y=28z\)
\(\Rightarrow\dfrac{x}{35}=\dfrac{y}{28}=\dfrac{z}{15}\)
\(\Rightarrow\dfrac{x^3}{35^3}=\dfrac{y^3}{28^3}=\dfrac{z^3}{15^3}=\dfrac{xyz}{35.28.15}=\dfrac{14700}{14700}=1\)
\(\Rightarrow\left\{{}\begin{matrix}x=35\\y=28\\z=15\end{matrix}\right.\)
\(12x=15y=28z\Rightarrow\dfrac{x}{\dfrac{1}{12}}=\dfrac{y}{\dfrac{1}{15}}=\dfrac{z}{\dfrac{1}{28}}\)
Đặt \(\dfrac{x}{\dfrac{1}{12}}=\dfrac{y}{\dfrac{1}{15}}=\dfrac{z}{\dfrac{1}{28}}=k\Rightarrow x=\dfrac{1}{12}k;y=\dfrac{1}{15}k;z=\dfrac{1}{28}k\)
\(xyz=14700\\ \Rightarrow\dfrac{1}{12}k\cdot\dfrac{1}{15}k\cdot\dfrac{1}{28}k=14700\\ \Rightarrow\dfrac{1}{5040}k^3=14700\\ \Rightarrow k^3=74088000\\ \Rightarrow k=420\\ \Rightarrow\left\{{}\begin{matrix}x=35\\y=28\\z=15\end{matrix}\right.\)
