Question

tìm x,y,z biết:

x/7=y/2 và y/3=z/5 với x+y-z=2/3

 

Answer 1

Ta có : \(\dfrac{x}{7}=\dfrac{y}{2}\Leftrightarrow\dfrac{x}{7}\cdot\dfrac{1}{3}=\dfrac{y}{2}\cdot\dfrac{1}{3}\Leftrightarrow\dfrac{x}{21}=\dfrac{y}{6}\)

và \(\dfrac{y}{3}=\dfrac{z}{5}\Leftrightarrow\dfrac{y}{3}\cdot\dfrac{1}{2}=\dfrac{z}{5}\cdot\dfrac{1}{2}\Leftrightarrow\dfrac{y}{6}=\dfrac{z}{10}\)

Áp dụng tính chất của dãy tỉ số bằng nhau :

\(\Rightarrow\dfrac{x}{21}=\dfrac{y}{6}=\dfrac{z}{10}=\dfrac{x+y-z}{21+6-10}=\dfrac{\dfrac{2}{3}}{17}=\dfrac{2}{51}\)

\(\Rightarrow\left\{{}\begin{matrix}x=\dfrac{2}{51}\cdot21=\dfrac{14}{17}\\y=\dfrac{2}{51}\cdot6=\dfrac{4}{17}\\z=\dfrac{2}{51}\cdot10=\dfrac{20}{51}\end{matrix}\right.\)