Question

Tìm x, y, z biết

\(\dfrac{x}{3}=\dfrac{y}{5};\dfrac{z}{7}=\dfrac{y}{3}\) và x - y = -12

Answer 1

\(\dfrac{x}{3}=\dfrac{y}{5},\dfrac{z}{7}=\dfrac{y}{5}\)

\(\Leftrightarrow\dfrac{x}{9}=\dfrac{y}{15};\dfrac{z}{35}=\dfrac{y}{15}\)

\(\Leftrightarrow\dfrac{x}{9}=\dfrac{y}{15}=\dfrac{z}{35}\)

Áp dụng t/c dãy tỉ số bằng nhau ta có :

\(\dfrac{x}{9}=\dfrac{y}{15}=\dfrac{z}{35}=\dfrac{x-y}{9-15}=\dfrac{-12}{-6}=2\)

\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{x}{9}=2\\\dfrac{y}{15}=2\\\dfrac{z}{35}=2\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=18\\y=30\\z=70\end{matrix}\right.\)

Vậy ........

Answer 2

\(\dfrac{x}{3}\)=\(\dfrac{y}{5}\);\(\dfrac{z}{7}\)=\(\dfrac{y}{3}\)

\(\rightarrow\)\(\dfrac{x}{9}\)=\(\dfrac{y}{15}\);\(\dfrac{z}{35}\)=\(\dfrac{y}{15}\)

\(\rightarrow\)\(\dfrac{x}{9}=\dfrac{y}{15}=\dfrac{z}{35}\)

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

\(\dfrac{x}{9}=\dfrac{y}{15}=\dfrac{z}{35}=\dfrac{x-y}{9-15}=\dfrac{-12}{-6}=2\)

\(\rightarrow\) \(\dfrac{x}{9}=2\rightarrow x=18\)

\(\rightarrow\dfrac{y}{15}=2\rightarrow y=30\)

\(\rightarrow\dfrac{z}{35}=2\rightarrow z=70\)

Vậy x=18

y=30

z=70