Ta có :
+, \(\frac{x}{4}=\frac{y}{3}\Leftrightarrow\frac{x}{8}=\frac{y}{6}\left(1\right)\)
+, \(\frac{y}{2}=\frac{z}{5}\Leftrightarrow\frac{y}{6}=\frac{z}{15}\left(2\right)\)
Từ \(\left(1\right)+\left(2\right)\Leftrightarrow\frac{x}{8}=\frac{y}{6}=\frac{z}{15}\)
Theo tính chất dãy tỉ số bằng nhau ta có :
\(\frac{x}{8}=\frac{y}{6}=\frac{z}{15}=\frac{x+y+z}{8+6+15}=\frac{5}{29}\)
\(\Leftrightarrow\left\{{}\begin{matrix}\frac{x}{8}=\frac{5}{29}\\\frac{y}{6}=\frac{5}{29}\\\frac{z}{15}=\frac{5}{29}\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=\frac{40}{29}\\x=\frac{30}{29}\\z=\frac{75}{29}\end{matrix}\right.\)
Vậy...
Theo đề ta có: \(\frac{x}{4}=\frac{y}{3};\frac{y}{2}=\frac{z}{5};x+y+z=5\)
Vì: \(\frac{x}{4}=\frac{y}{3}\Rightarrow\frac{x}{8}=\frac{y}{6}\) (1)
\(\frac{y}{2}=\frac{z}{5}\Rightarrow\frac{y}{6}=\frac{z}{15}\) (2)
Từ (1) và (2), ta suy ra:
\(\frac{x}{8}=\frac{y}{6}=\frac{z}{15}\)
Theo tính chất dãy tỉ sô bằng nhau ta có:
\(\frac{x}{8}=\frac{y}{6}=\frac{z}{15}\)\(=\frac{x+y+z}{8+6+15}=\frac{5}{29}\)
x/8 = 5/29 => x = 5/29 . 8 = 40/29
y/6 = 5/29 => y = 5/29 . 6 = 30/29
z/15 = 5/29 => z = 5/29 . 15 = 75/29
Ta có:
\(\frac{x}{4}=\frac{y}{3}\Rightarrow\frac{x}{8}=\frac{y}{6}.\)
\(\frac{y}{2}=\frac{z}{5}\Rightarrow\frac{y}{6}=\frac{z}{15}.\)
=> \(\frac{x}{8}=\frac{y}{6}=\frac{z}{15}\) và \(x+y+z=5.\)
Áp dụng tính chất dãy tỉ số bằng nhau ta được:
\(\frac{x}{8}=\frac{y}{6}=\frac{z}{15}=\frac{x+y+z}{8+6+15}=\frac{5}{29}.\)
\(\left\{{}\begin{matrix}\frac{x}{8}=\frac{5}{29}\Rightarrow x=\frac{5}{29}.8=\frac{40}{29}\\\frac{y}{6}=\frac{5}{29}\Rightarrow y=\frac{5}{29}.6=\frac{30}{29}\\\frac{z}{15}=\frac{5}{29}\Rightarrow z=\frac{5}{29}.15=\frac{75}{29}\end{matrix}\right.\)
Vậy \(\left(x;y;z\right)=\left(\frac{40}{29};\frac{30}{29};\frac{75}{29}\right).\)
Chúc bạn học tốt!
