Question

Tìm A U B ,A giao B,A\B với A={xϵ Z/ 3x+8/x+1ϵZ} , B={xϵN/(trị tuyệt đối của x+2)<5}

Answer 1

\(\frac{3x+8}{x+1}=3+\frac{5}{x+1}\) ĐKXĐ: \(x\ne-1\)

để \(\frac{3x+8}{x+1}\in Z\Leftrightarrow x+1\inƯ_{\left(5\right)}=\left\{\pm1;\pm5\right\}\)

\(\Rightarrow\left\{{}\begin{matrix}x=0\\x=-2\\x=4\\x=-6\end{matrix}\right.\)

\(\Rightarrow A=\left\{-2;-6;0;4\right\}\)

\(B=\left\{x\in N|\left|x+2\right|< 5\right\}\)

\(\Leftrightarrow\left[{}\begin{matrix}x+2< 5\\x+2< -5\end{matrix}\right.\) (x+2<-5 loại vì \(x\in N\) )

\(\Rightarrow B=\left\{0;1;2\right\}\)

\(\Rightarrow A\cup B=\left\{0;1;2;-2;-6;4\right\}\)

\(A\cap B=\left\{0\right\}\)

A\B={-2;-6;4}