a: Để phương trình có nghiệm thì \(\left\{{}\begin{matrix}m^2-3>=-1\\m^2-3< =1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}m^2>=2\\m^2< =4\end{matrix}\right.\)
\(\Leftrightarrow2< =m^2< =4\)
\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{2}< =m< =2\\-\sqrt{2}>=m>=-2\end{matrix}\right.\)
b: \(\Leftrightarrow\sin\left(2x+1\right)=-\sin\left(x-1\right)=\sin\left(1-x\right)\)
\(\Leftrightarrow\left[{}\begin{matrix}2x+1=1-x+k2\Pi\\2x+1=\Pi-1+x+k2\Pi\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}3x=k2\Pi\\3x=\Pi+k2\Pi-2\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{k2\Pi}{3}\\x=\dfrac{1}{3}\left(\Pi+k2\Pi-2\right)\end{matrix}\right.\)
