Question

/ 2x + 3 / + / 3y - 1/ + / x+y+z/ = 0

/= giá trị tuyệt đối

Answer 1

Ta có: \(\left\{{}\begin{matrix}\left|2x+3\right|\ge0\\\left|3y-1\right|\ge0\\\left|x+y+z\right|\ge0\end{matrix}\right.\)

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

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

\(\Leftrightarrow\left\{{}\begin{matrix}x=-\dfrac{3}{2}\\y=\dfrac{1}{3}\\z=0-\dfrac{1}{3}+\dfrac{3}{2}=\dfrac{7}{6}\end{matrix}\right.\)