Question

CMR : nếu 2 . ( x + y ) = 5 . ( y + z ) = 3 . ( z + x ) thì \(\frac{x-y}{4}=\frac{y-z}{5}\)

Answer 1

2 . ( x + y ) = 5 . ( y + z ) = 3 . ( z + x )

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

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

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

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

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