Solution 40 Page 16 Math Workbook 10 – Kite>

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Topic

Represent the set \(A = \left\{ {x \in \mathbb{R}|{x^2} \ge 9} \right\}\) as a union of half-intervals

Detailed explanation

We have: \({x^2} \ge 9\)\( \Leftrightarrow \left| x \right| \ge 3 \Leftrightarrow \left[ {\begin{array}{*{20}{c}}{x \ge 3}\\{x \le  – 3}\end{array}} \right.\)

Suy ra \(A = \{ x \in \mathbb{R}\left| {x \le  – 3} \right.\) hoặc \(x \le  – 3\}  = \{ x \in \mathbb{R}\left| {x \le  – 3\}  \cup } \right.\{ x \in \mathbb{R}\left| {x \ge 3\} } \right. = \left( { – \infty ; – 3} \right] \cup \left[ {3; + \infty } \right)\)

Vậy \(A = \left( { – \infty ; – 3} \right] \cup \left[{3;+\infty}\right)\)[{3;+\infty}\right)\)

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