a.
Do \(-1\le sin2x\le1\) nên pt có nghiệm khi:
\(-1\le\dfrac{m+3}{2m-1}\le1\) \(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{m+3}{2m-1}+1\ge0\\\dfrac{m+3}{2m-1}-1\le0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{3m+2}{2m-1}\ge0\\\dfrac{4-m}{2m-1}\le0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}m\le-\dfrac{2}{3}\\m\ge4\end{matrix}\right.\)
b.
Tương tự, pt có nghiệm khi:
\(-1\le\dfrac{m^2-3m+1}{m+1}\le1\)
\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{m^2-3m+1}{m+1}+1\ge0\\\dfrac{m^2-3m+1}{m+1}-1\le0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{m^2-2m+2}{m+1}\ge0\\\dfrac{m^2-4m}{m+1}\le0\end{matrix}\right.\)
\(\Leftrightarrow0\le m\le4\)
c.
\(0\le2cos^22x\le2\) nên pt có nghiệm khi:
\(0\le\dfrac{3m+1}{m-2}\le2\)
\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{3m+1}{m-2}\ge0\\\dfrac{3m+1}{m-2}-2\le0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{3m+1}{m-2}\ge0\\\dfrac{m+5}{m-2}\le0\end{matrix}\right.\)
\(\Leftrightarrow-5\le m\le-\dfrac{1}{3}\)
