Question

1. Tìm m để phương trình \(x^2-2\left(m-2\right)x+9>0\) với mọi x>1

Answer 1

\(\Delta'=\left(m-2\right)^2-9=\left(m-5\right)\left(m+1\right)\)

TH1: \(\Delta'< 0\Leftrightarrow-1< m< 5\)

TH2: \(\left\{{}\begin{matrix}\Delta'=0\\-\frac{b}{2a}\le1\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}\left[{}\begin{matrix}m=-1\\m=5\end{matrix}\right.\\m\le3\end{matrix}\right.\) \(\Rightarrow m=-1\)

TH3: \(\left\{{}\begin{matrix}\Delta>0\\f\left(1\right)\ge0\\-\frac{b}{2a}\le1\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}\left[{}\begin{matrix}m>5\\m< -1\end{matrix}\right.\\m\le7\\m\le3\end{matrix}\right.\) \(\Rightarrow m< -1\)

Vậy \(m< 5\)

Answer 2

@Phạm Minh Quang phương trình??