Bài 36 :
\(A=\left\{x\in R|\dfrac{1}{\left|x-2\right|}>\dfrac{1}{2}\right\}\)
Giải Bpt \(\dfrac{1}{\left|x-2\right|}>\dfrac{1}{2}\)
\(\Leftrightarrow\left|x-2\right|< 2\)
\(\Leftrightarrow\left\{{}\begin{matrix}x-2>-2\\x-2< 2\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x>0\\x< 4\end{matrix}\right.\) \(\Leftrightarrow0< x< 4\)
\(\Rightarrow A=\left\{x\in R|0< x< 4\right\}\)
\(B=\left\{x\in R|1\le\left|x\right|\le2\right\}\)
Giải Bpt \(1\le\left|x\right|\le2\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\le-1\cup x\ge1\\-2\le x\le2\end{matrix}\right.\)
\(\Leftrightarrow-2\le x\le-1\cup1\le x\le2\)
\(\Rightarrow B=\left\{x\in R|-2\le x\le-1\cup1\le x\le2\right\}\)
\(\Rightarrow A\cup B=\left[-2;-1\right]\cup(0;4)\)
\(A\cap B=(0;2]\)
\(\Rightarrow\left(A\cup B\right)\)\\(\left(A\cap B\right)=\left[-2;-1\right]\cup\left(2;4\right)\)
