\(2x=3y=5z\\ =>\dfrac{2x}{30}=\dfrac{3y}{30}=\dfrac{5z}{30}\\ =>\dfrac{x}{15}=\dfrac{y}{10}=\dfrac{z}{6}\)
mà `x-y=12` nên áp dụng tính chất dãy tỉ số bằng nhau ta có
`\(\dfrac{x}{15}=\dfrac{y}{10}=\dfrac{z}{6}=\dfrac{x-y}{15-10}=\dfrac{12}{5}=2,4\\ \dfrac{x}{15}=2,4=>x=36\\ \dfrac{y}{10}=2,4 =>y=24\\ \dfrac{z}{6}=2,4=>x=14,4\)
\(2x=3y=5z\Rightarrow\dfrac{x}{\dfrac{1}{2}}=\dfrac{y}{\dfrac{1}{3}}=\dfrac{z}{\dfrac{1}{5}}\)
Áp dụng tính chất dãy tỉ số bằng nhau ta có:
\(\dfrac{x}{\dfrac{1}{2}}=\dfrac{y}{\dfrac{1}{3}}=\dfrac{z}{\dfrac{1}{5}}=\dfrac{x-y}{\dfrac{1}{2}-\dfrac{1}{3}}=\dfrac{12}{\dfrac{1}{6}}=72\\ \dfrac{x}{\dfrac{1}{2}}=72\Rightarrow x=72.\dfrac{1}{2}\Rightarrow x=36\\ \dfrac{y}{\dfrac{1}{3}}=72\Rightarrow y=72.\dfrac{1}{3}\Rightarrow y=24\\ \dfrac{z}{\dfrac{1}{5}}=72\Rightarrow z=72.\dfrac{1}{5}\Rightarrow z=14,4\)
Vậy x=36;y=24;z=14,4
