Có: \(\frac{2}{3x}=\frac{4}{5y}=\frac{5}{6z}\Rightarrow\frac{3x}{\frac{1}{2}}=\frac{5y}{\frac{1}{4}}=\frac{6z}{\frac{1}{5}}\Rightarrow\frac{x}{\frac{1}{6}}=\frac{y}{\frac{1}{20}}=\frac{z}{\frac{1}{30}}\)
Áp dụng tính chất của dãy tỉ số bằng nhau ta có:
\(\frac{x}{\frac{1}{6}}=\frac{y}{\frac{1}{20}}=\frac{z}{\frac{1}{30}}=\frac{x+y+z}{\frac{1}{6}+\frac{1}{20}+\frac{1}{30}}=\frac{156}{\frac{1}{4}}=624\)
\(\Rightarrow\left\{{}\begin{matrix}\frac{x}{\frac{1}{6}}=624\Rightarrow x=624\cdot\frac{1}{6}=104\\\frac{y}{\frac{1}{20}}=624\Rightarrow y=624\cdot\frac{1}{20}=31,2\\\frac{z}{\frac{1}{30}}=624\Rightarrow z=624\cdot\frac{1}{30}=20,8\end{matrix}\right.\)
Vậy \(\left(x;y;z\right)=\left(104;31,2;20,8\right)\)