\(\hept{\begin{cases}\frac{x}{2}=\frac{y}{3}\\\frac{y}{4}=\frac{z}{5}\end{cases}}\)\(\Rightarrow\hept{\begin{cases}\frac{x}{8}=\frac{y}{12}\\\frac{y}{12}=\frac{z}{15}\end{cases}}\)\(\Rightarrow\frac{x}{8}=\frac{y}{12}=\frac{z}{15}\)
\(\Rightarrow\frac{x^2}{64}=\frac{y^2}{144}=\frac{z^2}{225}=\frac{x^2-y^2}{64-144}=\frac{-16}{-80}=\frac{1}{5}\)
\(\Rightarrow\hept{\begin{cases}x^2=\frac{1}{5}.64=12,8\\y^2=\frac{1}{5}.144=28,8\\z^2=\frac{1}{5}.225=45\end{cases}}\)\(\Rightarrow\hept{\begin{cases}x=\pm\sqrt{12,8}\\y=\pm\sqrt{28,8}\\z=\pm\sqrt{45}\end{cases}}\)
Với \(x=\sqrt{12,8}\Rightarrow\hept{\begin{cases}y=\sqrt{28,8}\\z=\sqrt{45}\end{cases}}\)
Với \(x=-\sqrt{12,8}\Rightarrow\hept{\begin{cases}y=-\sqrt{28,8}\\z=-\sqrt{45}\end{cases}}\)