Question

Tìm x,y,z:

\(\dfrac{x}{3}\)=\(\dfrac{y}{4}\);\(\dfrac{y}{5}\)=\(\dfrac{z}{7}\) và 2x + 3y - z=186

Answer 1

Ta có: \(\dfrac{x}{3}=\dfrac{y}{4}\Rightarrow\dfrac{x}{15}=\dfrac{y}{20}\)

\(\dfrac{y}{5}=\dfrac{z}{7}\Rightarrow\dfrac{y}{20}=\dfrac{z}{28}\)

\(\Rightarrow\dfrac{x}{15}=\dfrac{y}{20}=\dfrac{z}{28}\)

Áp dụng tính chất dãy tỉ số bằng nhau ta có:

\(\dfrac{x}{15}=\dfrac{y}{20}=\dfrac{y}{28}=\dfrac{2x+3y-z}{15\cdot2+3\cdot20-28}=\dfrac{186}{62}=3\)

\(\Rightarrow\left\{{}\begin{matrix}\dfrac{x}{15}=3\Rightarrow x=45\\\dfrac{y}{20}=3\Rightarrow y=60\\\dfrac{z}{28}=3\Rightarrow z=84\end{matrix}\right.\)

Vậy: ... 

Answer 2

 

 

�3=�4;�5=�7⇒�15=�20;�20=�283x​=4y​;5y​=7z​⇒15x​=20y​;20y​=28z​

Áp dụng tính chất dãy tỉ số bằng nhau :

�15=�20=�28=2�+3�−�30+60−28=18662=315x​=20y​=28z​=30+60−282x+3y−z​=62186​=3

⇒�15=3.15=45⇒15x​=3.15=45

⇒�20=3.20=60⇒20y​=3.20=60

⇒�28=3.28=84⇒28z​=3.28=84

Vậy x = 45; y= 60; z = 84