a) Ta có:
\(\dfrac{x}{10}=\dfrac{y}{6}=\dfrac{z}{21}\)
\(=\dfrac{5x}{50}=\dfrac{y}{6}=\dfrac{2z}{42}\)
Áp dụng tính chất dãy tỉ số bằng nhau ta được
\(\dfrac{5x}{50}=\dfrac{y}{6}=\dfrac{2z}{42}=\dfrac{5x+y-2z}{50+6-42}=\dfrac{28}{14}=2\)
\(\Rightarrow\left\{{}\begin{matrix}\dfrac{x}{10}=2\\\dfrac{y}{6}=2\\\dfrac{z}{21}=2\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x=20\\y=12\\z=42\end{matrix}\right.\)
b) Ta có:
\(2x=3y\)
\(\Rightarrow\dfrac{x}{3}=\dfrac{y}{2}\)
\(\Rightarrow\dfrac{x}{21}=\dfrac{y}{14}\left(1\right)\)
Ta lại có:
\(5y=7z\)
\(\Rightarrow\dfrac{y}{7}=\dfrac{z}{5}\)
\(\Rightarrow\dfrac{y}{14}=\dfrac{z}{10}\left(2\right)\)
Từ (1) và (2) suy ra:
\(\dfrac{x}{21}=\dfrac{y}{14}=\dfrac{z}{10}\)
\(=\dfrac{3x}{63}=\dfrac{5y}{70}=\dfrac{7z}{70}=\dfrac{3x+5y-7z}{63+70-70}=\dfrac{30}{63}=\dfrac{10}{21}\)
\(\Rightarrow\left\{{}\begin{matrix}\dfrac{x}{21}=\dfrac{10}{21}\\\dfrac{y}{14}=\dfrac{10}{21}\\\dfrac{z}{10}=\dfrac{10}{21}\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x=10\\y=\dfrac{20}{3}\\z=\dfrac{100}{21}\end{matrix}\right.\)
a, \(\dfrac{x}{10}=\dfrac{y}{6}=\dfrac{z}{21}\&5x+y-2z=28\)
\(\Rightarrow\dfrac{5x}{50}=\dfrac{y}{6}=\dfrac{2z}{42}\)
Áp dụng tính chất dãy tỉ số bằng nhau:
\(\dfrac{5x}{50}=\dfrac{y}{6}=\dfrac{2z}{42}=\dfrac{5x+y-2z}{50+6-42}=\dfrac{28}{14}=2\)
\(\Rightarrow\left\{{}\begin{matrix}\dfrac{x}{10}=2\\\dfrac{y}{6}=2\\\dfrac{z}{21}=2\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=20\\y=12\\z=42\end{matrix}\right.\)
b, \(2x=3y;5y=7z\&3x+5y-7z=30\)
Ta có: \(\left\{{}\begin{matrix}2x=3y\\5y=7z\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}\dfrac{x}{3}=\dfrac{y}{2}\\\dfrac{y}{7}=\dfrac{z}{5}\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}\dfrac{x}{21}=\dfrac{y}{14}\\\dfrac{y}{14}=\dfrac{z}{10}\end{matrix}\right.\Rightarrow\dfrac{x}{21}=\dfrac{y}{14}=\dfrac{z}{10}\)
\(\Rightarrow\dfrac{3x}{63}=\dfrac{5y}{70}=\dfrac{7z}{70}\)
Áp dụng tính chất dãy tỉ số bằng nhau:
\(\dfrac{3x}{63}=\dfrac{5y}{70}=\dfrac{7z}{70}=\dfrac{3x+5y-7z}{63+70-70}=\dfrac{30}{63}=\dfrac{10}{21}\)
\(\Rightarrow\left\{{}\begin{matrix}\dfrac{x}{21}=\dfrac{10}{21}\\\dfrac{y}{14}=\dfrac{10}{21}\\\dfrac{z}{10}=\dfrac{10}{21}\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=10\\y=\dfrac{20}{3}\\z=\dfrac{100}{21}\end{matrix}\right.\)
