Question

\(\dfrac{x}{3}\)=\(\dfrac{y}{4}\)=\(\dfrac{z}{5}\)  và x - 2y + 3z = 35

Answer 1

\(\dfrac{x}{3}=\dfrac{y}{4}=\dfrac{z}{5}< =>\dfrac{x}{3}=\dfrac{2y}{8}=\dfrac{3z}{15}\)

áp dụng tính chất dãy tỉ số = nhau

\(=>\dfrac{x}{3}=\dfrac{2y}{8}=\dfrac{3z}{15}=\dfrac{x-2y+3z}{3-8+15}=\dfrac{35}{10}=3,5\)

\(=>\dfrac{x}{3}=3.5=>x=10,5\)

\(\dfrac{2y}{8}=3,5=>y=14\)

\(\dfrac{3z}{15}=3,5=>z=17,5\)

Answer 2

\(\dfrac{x}{3}=\dfrac{y}{4}=\dfrac{z}{5}\Leftrightarrow\dfrac{x}{3}=\dfrac{2y}{8}=\dfrac{3z}{15}=\dfrac{x-2y+3z}{3-8+15}=\dfrac{35}{10}\)

- \(\dfrac{35}{10}=\dfrac{x}{3}\Rightarrow x=\dfrac{21}{2}\)

- \(\dfrac{35}{10}=\dfrac{y}{4}\Rightarrow y=14\)

-\(\dfrac{35}{10}=\dfrac{z}{5}\Rightarrow z=\dfrac{35}{2}\)

Tick cho mình với.

Answer 3

Ta có: \(\dfrac{x}{3}=\dfrac{y}{4}=\dfrac{z}{5}\)

nên \(\dfrac{x}{3}=\dfrac{2y}{8}=\dfrac{3z}{15}\)

Áp dụng tính chất của dãy tỉ số bằng nhau, ta được:

\(\dfrac{x}{3}=\dfrac{2y}{8}=\dfrac{3z}{15}=\dfrac{x-2y+3z}{3-8+15}=\dfrac{35}{10}=\dfrac{7}{2}\)

Do đó: \(\left\{{}\begin{matrix}x=\dfrac{21}{2}\\y=14\\z=\dfrac{35}{2}\end{matrix}\right.\)