\[\begin{array}{l}A = \left[ {0;4} \right],B = \left\{ {x \in R|{x^2} < 32} \right\},\\C = \left\{ {x \in R|{{\left[ {x - 2} \right]}^2} > 3} \right\},D = \left[ {\sqrt 6 ; + \infty } \right]\end{array}\]
Đề bài
Cho
\[\begin{array}{l}A = \left[ {0;4} \right],B = \left\{ {x \in R|{x^2} < 32} \right\},\\C = \left\{ {x \in R|{{\left[ {x - 2} \right]}^2} > 3} \right\},D = \left[ {\sqrt 6 ; + \infty } \right]\end{array}\]
Tìm \[\left[ {A \cap B} \right] \cup \left[ {C \cap D} \right]\]
Lời giải chi tiết
\[A\left[ {0;4} \right];B = \left[ { - 4\sqrt 2 ;4\sqrt 2 } \right].\] Vậy \[A \cap B = \left[ {0;4} \right]\]
\[\begin{array}{l}C = \left[ { - \infty ;2 - \sqrt 3 } \right] \cup \left[ {2 + \sqrt 3 ; + \infty } \right];\\D = \left[ {\sqrt 6 ; + \infty } \right].\end{array}\]
Vậy \[C \cap D = \left[ {2 + \sqrt 3 ; + \infty } \right]\]
Vậy \[\left[ {A \cap B} \right] \cup \left[ {C \cap D} \right] = \left[ {0; + \infty } \right]\].