Đáp án:
Giải thích các bước giải:
1.
\(\begin{array}{l}
Do: - 4{x^2} + 5x - 2 < 0\forall x \in R\\
\to f\left( x \right) > 0\forall x\\
\Leftrightarrow - {x^2} + 4\left( {m + 1} \right)x + 1 - 4{m^2} < 0\forall x\\
\Leftrightarrow \left\{ \begin{array}{l}
- 1 < 0\left( {ld} \right)\\
4\left( {{m^2} + 2m + 1} \right) + 1 - 4{m^2} < 0
\end{array} \right.\\
\Leftrightarrow 8m + 5 < 0\\
\Leftrightarrow m < - \frac{5}{8}
\end{array}\)
\(\begin{array}{l}
2.f\left( x \right) > 0\\
\Leftrightarrow \sqrt {{x^2} - x + m} > 1\\
\Leftrightarrow {x^2} - x + m > 1\\
\Leftrightarrow {x^2} - x + m - 1 > 0\\
\to \left\{ \begin{array}{l}
1 > 0\left( {ld} \right)\\
1 - 4.\left( {m - 1} \right) < 0
\end{array} \right.\\
\to 1 - 4m + 4 < 0\\
\to m > \frac{5}{4}
\end{array}\)
