Question

Bài 1: Tìm x,y,z biết:

a) \(\left|1-2x\right|+\left|2-3y\right|+\left|3-4z\right|=0\)

b) \(x+y=x:y=5\left(x-y\right)\)

Answer 1

a) Ta có: \(\left|1-2x\right|+\left|2-3y\right|+\left|3-4z\right|\ge0\)

Mà \(\left|1-2x\right|+\left|2-3y\right|+\left|3-4z\right|=0\)

\(\Rightarrow\left[{}\begin{matrix}\left|1-2x\right|=0\\\left|2-3y\right|=0\\\left|3-4z\right|=0\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}1-2x=0\\2-3y=0\\3-4z=0\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}2x=1\\3y=2\\4z=3\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{1}{2}\\y=\dfrac{2}{3}\\z=\dfrac{3}{4}\end{matrix}\right.\)

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