Câu 401: Đặt \(f\left(x\right)=\left(m-3\right)x^2+\left(m+2\right)x-4>0\)
\(f\left(x\right)>0\) vô nghiệm \(\forall x\in R\)
\(\Rightarrow\left[{}\begin{matrix}m-3=0\\\left\{{}\begin{matrix}m-3< 0\\\left(m+2\right)^2+4.4\left(m-3\right)\le0\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}m=3\\\left\{{}\begin{matrix}m< 3\\m^2+4m+4+16m-48\le0\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}m=3\\\left\{{}\begin{matrix}m< 3\\m^2+20m-44\le0\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}m=3\\\left\{{}\begin{matrix}m< 3\\m\in\left[-22;2\right]\end{matrix}\right.\end{matrix}\right.\)
Vậy BPT vô nghiệm khi \(m\in\left[-22;2\right]\)
Câu 396: Đặt \(f\left(x\right)=\left(m+2\right)x^2-2\left(m-1\right)x+m-3< 0\)
\(f\left(x\right)< 0\) vô nghiệm \(\forall x\in R\)
\(\Rightarrow\left[{}\begin{matrix}m+2=0\\\left\{{}\begin{matrix}m+2>0\\\left[-2\left(m-1\right)\right]^2-4\left(m+2\right)\left(m-3\right)\le0\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}m=-2\\\left\{{}\begin{matrix}m>-2\\4\left(m^2-2m+1\right)-4\left(m^2-m-6\right)\le0\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}m=-2\\\left\{{}\begin{matrix}m>-2\\4\left(m^2-2m+1-m^2+m+6\right)\le0\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}m=-2\\\left\{{}\begin{matrix}m>-2\\-m+7\le0\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}m=-2\\\left\{{}\begin{matrix}m>-2\\m\ge7\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}m=-2\\m\ge7\end{matrix}\right.\)
Vậy BPT vô nghiệm khi \(m\ge7\)
