Question

4cosx-3sinx=(m³-4m+3)x+m-4 tìm m để pt vô nghiệm.giúp với!!!!

Answer 1

\(4cosx-3sinx=5\left(\frac{4}{5}cosx-\frac{3}{5}sinx\right)=5cos\left(x+a\right)\) với \(cosa=\frac{4}{5}\)

\(\Rightarrow-5\le4cosx-3sinx\le5\)

\(\Rightarrow\) Pt vô nghiệm khi: \(\left[{}\begin{matrix}\left(m^3-4m+3\right)x+m-4>5\\\left(m^3-4m+3\right)+m-4< -5\end{matrix}\right.\) \(\forall x\)

\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}m^3-4m+3=0\\m-4>5\end{matrix}\right.\\\left\{{}\begin{matrix}m^3-4m+3=0\\m-4< -5\end{matrix}\right.\end{matrix}\right.\) \(\Rightarrow m=\frac{-1-\sqrt{13}}{2}\)