Question

Chứng minh rằng nếu 2(x+y) = 5(y+z) = 3(x+z) thì \(\dfrac{x-y}{4}\)=\(\dfrac{y-z}{5}\)

Answer 1

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

=> \(\dfrac{2\left(x+y\right)}{30}=\dfrac{5\left(y+z\right)}{30}=\dfrac{3\left(x+z\right)}{30}\)

=> \(\dfrac{x+y}{15}=\dfrac{y+z}{6}=\dfrac{x+z}{10}\)

Áp dụng t/c dãy tỉ số bằng nhau:

\(\dfrac{x+y}{15}=\dfrac{y+z}{6}=\dfrac{x+z}{10}=\dfrac{x+z-y-z}{10-6}=\dfrac{x+y-x-z}{15-10}=\dfrac{x-y}{4}=\dfrac{y-z}{5}\left(ĐPCM\right)\)