Question

Cho A=\([m+1,3m-2]\), B=\([2,2m+3]\)

a)tìm m để A\(\cap\)B khác \(\varnothing\)

b) tìm m để A\(\subset\)B

Answer 1

Lời giải:

a)

Để \(A\cap B\neq \varnothing \) thì :

\(\left\{\begin{matrix} (3m-2)-(m+1)>0\\ 2m+3-2>0\\ m+1\leq 2m+3\\ 3m-2\geq 2\end{matrix}\right.\Leftrightarrow \left\{\begin{matrix} m> \frac{3}{2}\\ m>\frac{-1}{2}\\ -2\leq m\\ m\geq \frac{4}{3}\end{matrix}\right.\Rightarrow m>\frac{3}{2}\)

b)

Để \(A\subset B\) thì \(\left\{\begin{matrix} (3m-2)-(m+1)>0\\ 2m+3-2>0\\ m+1\geq 2\\ 3m-2\leq 2m+3\end{matrix}\right.\Leftrightarrow \left\{\begin{matrix} m>\frac{3}{2}\\ m>\frac{-1}{2}\\ m\geq 1\\ m\leq 5\end{matrix}\right.\)

\(\Rightarrow 5\geq m>\frac{3}{2}\)