:vv
\(a,\) Áp dụng...
\(\dfrac{x}{3}=\dfrac{y}{4}=\dfrac{z}{5}=\dfrac{x-y-z}{3-4-5}=\dfrac{-24}{-6}=4\\ \Rightarrow\left\{{}\begin{matrix}x=12\\y=16\\z=20\end{matrix}\right.\)
\(b,\) Áp dụng...
\(\dfrac{x}{10}=\dfrac{y}{6}=\dfrac{z}{21}=\dfrac{5x}{50}=\dfrac{2z}{42}=\dfrac{5x+y-2z}{50+6-42}=\dfrac{28}{14}=2\\ \Rightarrow\left\{{}\begin{matrix}x=20\\y=12\\z=42\end{matrix}\right.\)
\(c,x:y:z=3:5:\left(-2\right)\Rightarrow\dfrac{x}{3}=\dfrac{y}{5}=\dfrac{z}{-2}\)
Áp dụng...
\(\dfrac{x}{3}=\dfrac{y}{5}=\dfrac{z}{-2}=\dfrac{5x}{15}=\dfrac{3z}{-6}=\dfrac{5x-y+3z}{15-5-6}=\dfrac{124}{4}=31\\ \Rightarrow\left\{{}\begin{matrix}x=93\\y=155\\z=-62\end{matrix}\right.\)
\(d,2x=3y=5z\Rightarrow\dfrac{2x}{30}=\dfrac{3y}{30}=\dfrac{5z}{30}\Rightarrow\dfrac{x}{15}=\dfrac{y}{10}=\dfrac{z}{6}\)
Áp dụng...
\(\dfrac{x}{15}=\dfrac{y}{10}=\dfrac{z}{6}=\dfrac{x+y-z}{15+10-6}=\dfrac{95}{19}=5\\ \Rightarrow\left\{{}\begin{matrix}x=75\\y=50\\z=30\end{matrix}\right.\)
