Question

Chung minh rang neu 2(x+y) = 5(y+z) = 3(z+x) thi \(\frac{x-y}{4}\) \(\frac{y-z}{5}\)

Answer 1

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

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

Áp dụng tính chất dãy tỉ số bằng nhau ta có: 

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

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

Suy ra đpcm.