Cho \({\rm{A = \{ }}x \in \mathbb{N},\,(2x - {x^2})(2{x^2} - 3x - 2) = 0\} \) và \({\rm{B = \{ n}} \in \mathbb{N},\,3 < {n^2} < 30\} \). Tìm kết quả phép toán \[{\rm{A}} \cap {\rm{B}}\].
Cho \({\rm{A = \{ }}x \in \mathbb{N},\,(2x - {x^2})(2{x^2} - 3x - 2) = 0\} \) và \({\rm{B = \{ n}} \in \mathbb{N},\,3 < {n^2} < 30\} \). Tìm kết quả phép toán \[{\rm{A}} \cap {\rm{B}}\].
Hãy suy nghĩ và trả lời câu hỏi trước khi xem đáp án
$(2x - x^2)(2x^2 - 3x - 2) = 0$
$=> x(2-x)(2x+1)(x-2)=0$
$=> x(x-2)^2(2x+1)=0$
Vì $x \in \mathbb{N}$ nên $x = 0$ hoặc $x = 2$. Do đó, $A = \{0, 2\}$.
Giải B:
$3 < n^2 < 30$
Vì $n \in \mathbb{N}$ nên $n \in \{2, 3, 4, 5\}$. Do đó, $B = \{2, 3, 4, 5\}$.
Vậy $A \cap B = \{2\}$
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