Question

Tìm x,y,z biết

2x=3y=4z, x+y-z= 28

Answer 1

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

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

\(\dfrac{x}{\dfrac{1}{2}}=\dfrac{y}{\dfrac{1}{3}}=\dfrac{z}{\dfrac{1}{4}}=\dfrac{x+y-z}{\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{4}}=\dfrac{28}{\dfrac{7}{12}}=48\)

\(\Rightarrow\left\{{}\begin{matrix}\dfrac{x}{\dfrac{1}{2}}=48\Rightarrow x=48\cdot\dfrac{1}{2}=24\\\dfrac{y}{\dfrac{1}{3}}=48\Rightarrow y=48\cdot\dfrac{1}{3}=16\\\dfrac{z}{\dfrac{1}{4}}=48\Rightarrow z=48\cdot\dfrac{1}{4}=12\end{matrix}\right.\)