by Cho $A=\left\{ x|\left( 2x-{{x}^{2}} \right)\left( 2{{x}^{2}}-3x-2 \right)=0 \right\}$ và $B=\left\{ n\in \mathbb{N}*|3<{{n}^{2}}<30 \right\}$. Khi đó, $A\cap B$ bằng.
A. $\left\{ 2;4 \right\}. $
B. $\left\{ 2 \right\}. $
C. $\left\{ 4;5 \right\}. $
D. $\left\{ 3 \right\}. $
Hướng dẫn
HD: $\left( {2x – {x^2}} \right)\left( {2{x^2} – 3x – 2} \right) = 0 \Leftrightarrow \left[ \begin{array}{l} 2x – {x^2} = 0\\ 2{x^2} – 3x – 2 = 0 \end{array} \right. \Leftrightarrow \left[ \begin{array}{l} x = 0\\ x = 2\\ x = – \frac{1}{2} \end{array} \right.$ $\Rightarrow A=\left\{ -\frac{1}{2};0;2 \right\}$ $\left\{ \begin{array}{l} n \in *\\ 3 < {n^2} < 30 \end{array} \right. \Leftrightarrow \left\{ \begin{array}{l} n \in *\\ \sqrt 3 < n < \sqrt {30} \end{array} \right. \Rightarrow B = \left\{ {2;3;4;5} \right\}$ $\Rightarrow A\cap B=\left\{ 2 \right\}. $ Chọn đáp án B.
