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Câu hỏi: Cho \(A = \left\{ {x \in R|\left| {x - 1} \right| < 3} \right\}\) và \(B = \left\{ {x \in R|\left| {x + 2} \right| > 5} \right\}.\)
Hãy tìm \(A \cap B.\)
Hãy tìm \(A \cap B.\)
Lời giải chi tiết
Ta có:
\(\begin{array}{l}\left| {x - 1} \right| < 3 \Leftrightarrow - 3 < x - 1 < 3\\ \Leftrightarrow \left\{ \begin{array}{l}x - 1 > - 3\\x - 1 < 3\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}x > - 2\\x < 4\end{array} \right.\\ \Leftrightarrow - 2 < x < 4\\ \Rightarrow A = \left( { - 2; 4} \right)\end{array}\)
\(\begin{array}{l}\left| {x + 2} \right| > 5 \Leftrightarrow \left[ \begin{array}{l}x + 2 > 5\\x + 2 < - 5\end{array} \right.\\ \Leftrightarrow \left[ \begin{array}{l}x > 3\\x < - 7\end{array} \right.\\ \Rightarrow B = \left( { - \infty ; - 7} \right) \cup \left({3; + \infty } \right)\end{array}\)
Vậy \(A \cap B = \left( {3; 4} \right)\)
Ta có:
\(\begin{array}{l}\left| {x - 1} \right| < 3 \Leftrightarrow - 3 < x - 1 < 3\\ \Leftrightarrow \left\{ \begin{array}{l}x - 1 > - 3\\x - 1 < 3\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}x > - 2\\x < 4\end{array} \right.\\ \Leftrightarrow - 2 < x < 4\\ \Rightarrow A = \left( { - 2; 4} \right)\end{array}\)
\(\begin{array}{l}\left| {x + 2} \right| > 5 \Leftrightarrow \left[ \begin{array}{l}x + 2 > 5\\x + 2 < - 5\end{array} \right.\\ \Leftrightarrow \left[ \begin{array}{l}x > 3\\x < - 7\end{array} \right.\\ \Rightarrow B = \left( { - \infty ; - 7} \right) \cup \left({3; + \infty } \right)\end{array}\)
Vậy \(A \cap B = \left( {3; 4} \right)\)