Tìm \(m\) để bất phương trình \(1 + {\log _5}\left...

C

- Hướng dẫn giải

BPT thoã mãn với mọi \(x \in \mathbb{R}\).Û \(\left\{ \begin{array}{l}m{x^2} + 4x + m > 0\\5\left( {{x^2} + 1} \right) \ge m{x^2} + 4x + m\end{array} \right.\left( {\forall x \in \mathbb{R}} \right)\) Û \(\left\{ \begin{array}{l}m{x^2} + 4x + m > 0\\\left( {5 - m} \right){x^2} - 4x + 5 - m \ge 0\end{array} \right.\left( {\forall x \in \mathbb{R}} \right)\) Û \(\left\{ \begin{array}{l}m > 0\\16 - 4{m^2} < 0\\5 - m > 0\\16 - 4{\left( {5 - m} \right)^2} \le 0\end{array} \right.\) Û \(\left\{ \begin{array}{l}m > 0\\\left[ \begin{array}{l}m <  - 2\\m > 2\end{array} \right.\\m < 5\\\left[ \begin{array}{l}m \le 3\\m \ge 7\end{array} \right.\end{array} \right.\) Û \(2 < m \le 3\).