Question

Cho A =\(\left\{x\in R|\left|mx-3\right|=mx-3\right\}\) , B=\(\left\{x\in R|x^2-4=0\right\}\).Tìm m để B\A = B 

Answer 1

\(\left|mx-3\right|=mx-3\Leftrightarrow mx-3\ge0\) \(\Rightarrow\left[{}\begin{matrix}x\ge\dfrac{3}{m}\left(m>0\right)\\x\le\dfrac{3}{m}\left(m< 0\right)\end{matrix}\right.\)

\(x^2-4=0\Rightarrow x=\pm2\Rightarrow B=\left\{-2;2\right\}\)

\(B\backslash A=B\Leftrightarrow A\cap B=\varnothing\)

\(\Rightarrow\left[{}\begin{matrix}\dfrac{3}{m}>2\left(m>0\right)\\\dfrac{3}{m}< -2\left(m< 0\right)\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}0< m< \dfrac{3}{2}\\-\dfrac{3}{2}< m< 0\end{matrix}\right.\)