Question

Chứng minh rằng : nếu \(2.\left(x+y\right)=5.\left(y+z\right)=3.\left(z+x\right)\)  thì \(\frac{x-y}{4}=\frac{y-2}{5}\)

 

Answer 1

\(2.\left(x+y\right)=5.\left(y+z\right)=3.\left(z+x\right)\)

\(\Rightarrow\text{ }\frac{2.\left(x+y\right)}{30}=\frac{5.\left(y+z\right)}{30}=\frac{3.\left(z+x\right)}{30}\)

\(\Rightarrow\text{ }\frac{x+y}{15}=\frac{y+z}{6}=\frac{z+x}{10}\)

\(\frac{x+y}{15}=\frac{z+x}{10}=\frac{\left(x+y\right)-\left(z+x\right)}{15-10}=\frac{y-z}{5}\text{ }\left(1\right)\)

\(\frac{z+x}{10}=\frac{y+z}{6}=\frac{\left(z+x\right)-\left(y+z\right)}{10-6}=\frac{x-y}{4}\text{ }\left(2\right)\)

Từ ( 1 ) và ( 2 ) \(\Rightarrow\text{ }\frac{y-z}{5}=\frac{x-y}{4}\)