Đáp án:
\(KL:x \in \left( { - \infty ;\dfrac{{3 - \sqrt {73} }}{2}} \right) \cup \left( {\dfrac{{3 + \sqrt {73} }}{2}; + \infty } \right)\)
Giải thích các bước giải:
\(\begin{array}{l}
\left| {x + 1} \right| + \left| {x - 4} \right| > 7\\
\to {x^2} + 2x + 1 + {x^2} - 8x + 16 > 49\\
\to 2{x^2} - 6x - 32 > 0\\
\to {x^2} - 3x - 16 > 0\\
Xét:{x^2} - 3x - 16 = 0\\
\to \left[ \begin{array}{l}
x = \dfrac{{3 + \sqrt {73} }}{2}\\
x = \dfrac{{3 - \sqrt {73} }}{2}
\end{array} \right.
\end{array}\)
BXD:
x -∞ \(\dfrac{{3 - \sqrt {73} }}{2}\) \(\dfrac{{3 + \sqrt {73} }}{2}\) +∞
f(x) + 0 - 0 +
\(KL:x \in \left( { - \infty ;\dfrac{{3 - \sqrt {73} }}{2}} \right) \cup \left( {\dfrac{{3 + \sqrt {73} }}{2}; + \infty } \right)\)
