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$(1) \Leftrightarrow \,\,\,\,7{x^2} + 7 \ge m{x^2} + 4x + m,\,\,\,\forall x \in \,R\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,$
$ \Leftrightarrow \left\{ \begin{array}{l}
\left( {7 - m} \right){x^2} - 4x + 7 - m \ge 0\,\,\,\,\,\,\,\,\,\,\,\,\,\,(2)\\
m{x^2} + 4x + m > 0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(3)
\end{array} \right.\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,$
$m = 7\,\,\,$ $(2)$ không thỏa mãn $\forall x\in R$
$m = 0$ $(3)$ không thỏa mãn $\forall x\in R$
$(1)$ thỏa mãn $\forall x\in R$ $ \Leftrightarrow \left\{ \begin{array}{l}
7 - m > 0\\
{\Delta _2}' = 4 - {\left( {7 - m} \right)^2} \le 0\\
m > 0\\
{\Delta _3}' = 4 - {m^2} < 0
\end{array} \right.$
$ \Leftrightarrow \left\{ \begin{array}{l}
m < 7\\
m \le 5\\
m > 0\\
m > 2
\end{array} \right.\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \Leftrightarrow 2 < m \le 5$
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