\(\frac{2x}{3}=\frac{2y}{4}=\frac{4z}{5}\)=> \(\frac{x}{\frac{3}{2}}=\frac{y}{\frac{4}{2}}=\frac{z}{\frac{5}{4}}\)=> \(\frac{x}{\frac{3}{2}}=\frac{y}{2}=\frac{z}{\frac{5}{4}}\)
Áp dụng t/c dãy tỉ số bằng nhau ta có :
\(\frac{x}{\frac{3}{2}}=\frac{y}{2}=\frac{z}{\frac{5}{4}}=\frac{x+y+z}{\frac{3}{2}+2+\frac{5}{4}}=\frac{49}{\frac{19}{4}}=\frac{196}{19}\)
=> \(\hept{\begin{cases}\frac{x}{\frac{3}{2}}=\frac{196}{19}\\\frac{y}{2}=\frac{196}{19}\\\frac{z}{\frac{5}{4}}=\frac{196}{19}\end{cases}\Rightarrow}\hept{\begin{cases}x=\frac{294}{19}\\y=\frac{392}{19}\\z=\frac{245}{19}\end{cases}}\)
Bài làm:
Ta có: \(\frac{2x}{3}=\frac{2y}{4}=\frac{4y}{5}\)
\(\Leftrightarrow\frac{x}{6}=\frac{y}{8}=\frac{z}{5}\)
Áp dụng t/c dãy tỉ số bằng nhau:
\(\frac{x}{6}=\frac{y}{8}=\frac{z}{5}=\frac{x+y+z}{6+8+5}=\frac{49}{19}\)
\(\Rightarrow\hept{\begin{cases}x=\frac{49}{19}.6=\frac{294}{19}\\y=\frac{49}{19}.8=\frac{392}{19}\\z=\frac{49}{19}.5=\frac{245}{19}\end{cases}}\)
Bài làm
\(\frac{2x}{3}=\frac{2y}{4}=\frac{4z}{5}=\frac{x}{\frac{3}{2}}=\frac{y}{\frac{4}{2}}=\frac{z}{\frac{5}{4}}=\frac{x+y+z}{\frac{3}{2}+\frac{4}{2}+\frac{5}{4}}=\frac{49}{\frac{19}{4}}=49\cdot\frac{4}{19}=\frac{196}{19}\)
\(\Rightarrow\hept{\begin{cases}x=\frac{196}{19}\cdot\frac{3}{2}=\frac{294}{19}\\y=\frac{196}{19}\cdot2=\frac{392}{19}\\z=\frac{196}{19}\cdot\frac{5}{4}=\frac{245}{19}\end{cases}}\)
Vậy \(x=\frac{294}{19}\text{ ; }y=\frac{392}{19}\text{ ; }z=\frac{245}{19}\)
Ta có :
\(\frac{2x}{3}=\frac{2y}{4}=\frac{4y}{5}\)
\(\Leftrightarrow\frac{x}{6}=\frac{y}{8}=\frac{z}{5}\)
Áp dụng tính chất dãy tỉ số bằng nhau :
\(\frac{x}{6}=\frac{y}{8}=\frac{z}{5}=\frac{x+y+z}{6+8+5}=\frac{49}{19}\)
\(\Rightarrow\hept{\begin{cases}x=\frac{49}{19}.6=\frac{294}{19}\\y=\frac{49}{19}.8=\frac{392}{19}\\z=\frac{49}{19}.5=\frac{245}{19}\end{cases}}\)
