Giải thích các bước giải:
\(\begin{array}{l}
a,\\
f\left( x \right) > 0,\,\,\,\forall x \in R\\
\Leftrightarrow {x^2} - \left( {m + 2} \right)x + 8m + 1 > 0,\,\,\,\forall x \in R\\
\Leftrightarrow Δ \le 0\\
\Leftrightarrow {\left( {m + 2} \right)^2} - 4.\left( {8m + 1} \right) \le 0\\
\Leftrightarrow {m^2} + 4m + 4 - 32m - 4 \le 0\\
\Leftrightarrow {m^2} - 28m \le 0\\
\Leftrightarrow 0 \le m \le 28\\
b,\\
g\left( x \right) > 0,\,\,\,\forall x \in R\\
\Leftrightarrow \left( {3m - 3} \right){x^2} - \left( {3m + 6} \right)x + m - 3 > 0,\,\,\,\forall x \in R\\
\Leftrightarrow \left\{ \begin{array}{l}
Δ \le 0\\
3m - 3 > 0
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
{\left( {3m + 6} \right)^2} - 4.\left( {3m - 3} \right)\left( {m - 3} \right) \le 0\\
m > 1
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
9{m^2} + 36m + 36 - 4.\left( {3{m^2} - 12m + 9} \right) \le 0\\
m > 1
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
- 3{m^2} + 84m \le 0\\
m > 1
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
\left[ \begin{array}{l}
m \ge \frac{{83}}{4}\\
m \le 0
\end{array} \right.\\
m > 1
\end{array} \right. \Rightarrow m \ge \frac{{83}}{4}
\end{array}\)
