Ta có :2x=4y=7z
=>\(\dfrac{2x}{28}=\dfrac{4y}{28}=\dfrac{7z}{28}\)
=>\(\dfrac{x}{14}=\dfrac{y}{7}=\dfrac{z}{4}\)
=>\(\dfrac{2x}{28}=\dfrac{3y}{21}=\dfrac{z}{4}\)
Áp dụng tính chất dãy tỉ số bằng nhau ,ta có
\(\dfrac{2x}{28}=\dfrac{3y}{21}=\dfrac{z}{4}=\dfrac{2x-3y-z}{28-21-4}=\dfrac{12}{3}=4\)(do 2x-3y-z=12)
Suy ra \(\dfrac{2x}{28}=\dfrac{x}{14}=3\)=>x=52
\(\dfrac{3y}{21}=\dfrac{y}{7}=3\)=>y=21
\(\dfrac{z}{4}=3\)=>z=12
Ta có: \(2x=4y=7z\)
\(\Rightarrow\dfrac{2x}{28}=\dfrac{4y}{28}=\dfrac{7z}{28}=k\left(k\in Q\right)\) \(\Rightarrow\dfrac{x}{14}=\dfrac{y}{7}=\dfrac{z}{4}=k\)
\(\Rightarrow\dfrac{2x}{28}=\dfrac{3y}{21}=\dfrac{z}{4}=k\)
Áp dụng tính chất của dãy tỉ số bằng nhau, ta có:
\(\dfrac{2x}{28}=\dfrac{3y}{21}=\dfrac{z}{4}=\dfrac{2x-3y-z}{28-21-4}=\dfrac{12}{3}=4\)
\(\Rightarrow\dfrac{x}{14}=\dfrac{y}{7}=\dfrac{z}{4}=4\)
\(\Rightarrow\left\{{}\begin{matrix}x=14.4\\y=7.4\\z=4.4\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x=56\\y=28\\z=16\end{matrix}\right.\)
Vậy \(x=56,y=28,z=16\)
