Question

Cho A ={ x|(2x-x²)(2x²-3x-2)=0}và B={n€N*|3<n²<30} Kkhi đó A giao B bằng

Answer 1

Lời giải:

Xét tập A

\((2x-x^2)(2x^2-3x-2)=0\)

\(\Leftrightarrow x(2-x)(x-2)(2x+1)=0\)

\(\Leftrightarrow -x(x-2)^2(2x+1)=0\)

\(\Rightarrow \left[\begin{matrix} x=0\\ x-2=0\\ 2x+1=0\end{matrix}\right.\Rightarrow \left[\begin{matrix} x=0\\ x=2\\ x=\frac{-1}{2}\end{matrix}\right.\)

Vậy \(A=\left\{0;2;\frac{-1}{2}\right\}\)

Xét B

\(3< n^2< 30\Rightarrow \sqrt{3}< n< \sqrt{30}\)

\(\Rightarrow 1< n< 6\)

Vì \(n\in\mathbb{N}^*\Rightarrow n\in \left\{2;3;4;5\right\}\)

Vậy \(B=\left\{2;3;4;5\right\}\)

Do đó \(A\cap B=\left\{2\right\}\)