Question

Tìm x; y; z biết:

\(\dfrac{x-1}{2}\)=\(\dfrac{y-2}{3}\)=\(\dfrac{z-3}{4}\) và x - 2y - 3z = 14

Answer 1

\(\dfrac{x-1}{2}=\dfrac{y-2}{3}=\dfrac{z-3}{4}\)

\(\Leftrightarrow\dfrac{x-1}{2}=\dfrac{-2y+4}{-6}=\dfrac{3z-9}{12}\)

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

\(\dfrac{x-1}{2}=\dfrac{-2y+4}{-6}=\dfrac{3z-9}{12}=\dfrac{x-1-2y+4+3z-9}{2-6+12}=\dfrac{\left(x-2y+3z\right)-6}{8}=\dfrac{14-6}{8}=1\)

\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{x-1}{2}=1\\\dfrac{y-2}{3}=1\\\dfrac{z-3}{4}=1\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x=3\\y=5\\z=7\end{matrix}\right.\)

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