Question

Tìm \(A\cap B;A\cup B;A/B;B/A\)
\(A=\left\{x\in Z|x^2< 4\right\};B=\left\{x\in Z|\left(5x-3x^2\right)\left(x^2-2x-3\right)=0\right\} \)

Answer 1

\(A=\left\{x\in Z,x^2< 4\right\}\)

\(\Rightarrow A=\left\{-1;0;1\right\}\)

\(B=\left\{x\in Z,\left(5x-3x^2\right)\left(x^2-2x-3\right)=0\right\}\)\(\Rightarrow\left[{}\begin{matrix}5x-3x^2=0\\x^2-2x-3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\frac{5}{3}\left(loai\right)\\x=0\\x=3\\x=-1\end{matrix}\right.\)

\(\Rightarrow B=\left\{0;-1;3\right\}\)

\(\Rightarrow A\cap B=\left\{0;-1\right\}\) \(A\cup B=\left\{0;-1;1;3\right\}\)

\(A\backslash B=\left\{1\right\}\) \(B\backslash A=\left\{3\right\}\)