Решите неравенство: 2x² – x – 55 > 0.

Ответ:

\[2x^{2} - x - 55 > 0\]

\[2x^{2} - x - 55 = 0\]

\[D = 1 + 440 = 441 = 21^{2}\]

\[x_{1} = \frac{1 + 21}{4} = \frac{22}{4} = 5,5\]

\[x_{2} = \frac{1 - 21}{4} = - \frac{20}{4} = - 5.\]

\[(x + 5)(x - 5,5) > 0\]

\[x \in ( - \infty; - 5) \cup (5,5; + \infty).\]