Question

Cho biết:3(x-y)=7(y-z)=5(z-x)

CMR:\(\frac{y-x}{9}=\frac{z-y}{14}\)

Answer 1

Có: 

\(3\left(x-y\right)=7\left(y-z\right)=5\left(z-x\right)\)

=> \(\frac{3\left(x-y\right)}{3.7.5}=\frac{7\left(y-z\right)}{3.7.5}=\frac{5\left(z-x\right)}{3.7.5}\)

=> \(\frac{x-y}{35}=\frac{y-z}{15}=\frac{z-x}{21}\)

Áp dụng dãy tỉ số bằng nhau ta có:

\(\frac{x-y}{35}=\frac{y-z}{15}=\frac{z-x}{21}=\frac{x-y+y-z+z-x}{35+15+21}=\frac{0}{71}=0\)

=> \(x=y=z\)

Suy ra: \(\frac{y-x}{9}=0=\frac{z-y}{14}\)