Giải thích các bước giải:
\(\begin{array}{l}
38,\\
\left( {m + 1} \right){x^2} + mx + m < 0,\,\,\,\,\forall x \in R\\
\Leftrightarrow \left\{ \begin{array}{l}
m + 1 < 0\\
Δ< 0
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
m < - 1\\
{m^2} - 4\left( {m + 1} \right).m < 0
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
m < - 1\\
m\left( {m - 4m - 4} \right) < 0
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
m < - 1\\
m.\left( {3m + 4} \right) > 0
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
m < - 1\\
\left[ \begin{array}{l}
m > 0\\
m < - \frac{4}{3}
\end{array} \right.
\end{array} \right. \Leftrightarrow m < - \frac{4}{3}\\
39,\,\,\,\,m < - \frac{4}{3}\\
40,\\
\left( {m - 1} \right){x^2} - 2\left( {m - 1} \right)x + m + 3 \ge 0,\,\,\,\,\forall x \in R\\
\Leftrightarrow \left\{ \begin{array}{l}
m - 1 > 0\\
Δ' \le 0
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
m > 1\\
{\left( {m - 1} \right)^2} - \left( {m - 1} \right).\left( {m + 3} \right) \le 0
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
m > 1\\
\left( {m - 1} \right).\left[ {\left( {m - 1} \right) - \left( {m + 3} \right)} \right] \le 0
\end{array} \right.\\
\Leftrightarrow m > 1
\end{array}\)
