Question

Tìm m để phương trình có nghiệm :

a) \(2sin\left(x+4\pi\right)=2m-1\).

b)sin(7-x)=\(5m+6m^2\) .

Answer 1

\(2sin\left(x+4\pi\right)=\frac{2m-1}{2}\)

\(\Rightarrow-1\le\frac{2m-1}{2}\le1\Rightarrow\frac{-1}{2}\le m\le\frac{3}{2}\)

\(sin\left(7-x\right)=5m+6m^2\)

\(\Rightarrow\left\{{}\begin{matrix}6m^2+5m\ge-1\\6m^2+5m\le1\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}6m^2+5m+1\ge0\\6m^2+5m-1\le0\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}\left[{}\begin{matrix}m\ge-\frac{1}{3}\\m\le-\frac{1}{2}\end{matrix}\right.\\-1\le m\le\frac{1}{6}\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}-1\le m\le-\frac{1}{2}\\-\frac{1}{3}\le m\le\frac{1}{6}\end{matrix}\right.\)