Question

For 2(x-y)=5(y+z)=3(x+z)

Prove that: \(\dfrac{x-y}{4}=\dfrac{y-z}{5}\)

I hope you will help me!

Answer 1

OK you. I will help

Giải

Chia mỗi hạng tử cho BCNN (3,5,2) = 30

\(\Rightarrow\)\(2\left(x-y\right)=5\left(y+x\right)=3\left(x+z\right)=\dfrac{2\left(x-y\right)}{30}=\dfrac{5\left(y+x\right)}{30}=\dfrac{3\left(x+z\right)}{30}=\dfrac{x-y}{15}=\dfrac{y+z}{6}=\dfrac{x+z}{10}\)

Áp dụng tính chất của dãy tỉ số bằng nhau, Ta có:

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

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

Từ (1) và (2) \(\Rightarrow\dfrac{y-z}{5}=\dfrac{x-y}{4}\left(đpcm\right)\)

Answer 2

hope you understand. Remember to brainstorm before asking questions. NHEO