\(\frac{x}{2}=\frac{y}{3}=\frac{z}{4}\)
=> \(\frac{x}{2}.\frac{x}{2}.\frac{x}{2}=\frac{y}{3}.\frac{y}{3}.\frac{y}{3}=\frac{z}{4}.\frac{y}{3}.\frac{x}{2}\)
=> \(\frac{x^3}{8}=\frac{y^3}{27}=\frac{xyz}{24}=\frac{14}{24}=\frac{7}{12}\)
=> \(x^3=\frac{14}{3}\Rightarrow x=\sqrt[3]{\frac{14}{3}}\)=> \(y=3.\frac{x}{2}=\sqrt[3]{\frac{63}{4}}\)và \(z=4.\frac{x}{2}=\sqrt[3]{\frac{112}{3}}\)
\(\frac{x}{2}=\frac{y}{3}=\frac{z}{4}\)và \(xyz=14\)
Đặt : \(\hept{\begin{cases}x=2k\\y=3k\\z=4k\end{cases}}\)
Thay x;y;z vào x.y.z = 14 ta đc
\(2k.3k.4k=14\)
\(\left(2.3.4\right)\left(k.k.k\right)=14\)
\(24k^3=14\Leftrightarrow k^3=\frac{7}{12}\Leftrightarrow k=\sqrt[3]{\frac{7}{12}}\)
Tự lắp vào tính x;y;z nhé !
