Tìm m để (left| {4x - 2m - frac{1}{2}} ight| > - {x^2} + 2x + frac{1}{2} - m) với mọi x?

* Hướng dẫn giải

\(\begin{array}{l}
\left| {4x - 2m - \frac{1}{2}} \right| >  - {x^2} + 2x + \frac{1}{2} - m\\
 \Leftrightarrow \left[ \begin{array}{l}
4x - 2m - \frac{1}{2} >  - {x^2} + 2x + \frac{1}{2} - m\\
4x - 2m - \frac{1}{2} < {x^2} - 2x - \frac{1}{2} + m
\end{array} \right.\\
 \Leftrightarrow \left[ \begin{array}{l}
{x^2} + 2x - m - 1 > 0\\
{x^2} - 6x + 3m > 0
\end{array} \right.\\
 \Leftrightarrow \left[ \begin{array}{l}
{1^2} + \left( {m + 1} \right) < 0\\
{3^2} - 3m < 0
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
m <  - 2\\
m > 3
\end{array} \right.
\end{array}\)