Câu 1 trang 238 SBT Đại số 10 Nâng cao

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 \(\left( {A \cap B} \right) \cup \left( {C \cap D} \right)\)

Giải:

\(A\left( {0;4} \right);B = \left( { - 4\sqrt 2 ;4\sqrt 2 } \right).\) 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 \(\left( {A \cap B} \right) \cup \left( {C \cap D} \right) = \left( {0; + \infty } \right)\).

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