Question

\(A=\left[a;a+2\right];B=\left[0;2019\right];C=\left\{x\in R:\frac{|x|-1}{|x|}>0\right\}\)

Tìm a để A\(\cap\)B\(\cap\)C=\(\phi\)

Answer 1

\(\frac{\left|x\right|-1}{\left|x\right|}>0\Leftrightarrow\left\{{}\begin{matrix}x\ne0\\\left|x\right|-1>0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x>1\\x< -1\end{matrix}\right.\)

\(\Rightarrow C=\left(-\infty;-1\right)\cup\left(1;+\infty\right)\)

\(\Rightarrow B\cap C=(1;2019]\)

\(\Rightarrow A\cap B\cap C=\varnothing\Leftrightarrow\left[{}\begin{matrix}a>2019\\a+2\le1\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}a>2019\\a\le-1\end{matrix}\right.\)