Решите неравенство: 6x² – x – 1 < 0.

Ответ:

\[6x^{2} - x - 1 < 0\]

\[6x^{2} - x - 1 = 0\]

\[D = 1 + 24 = 25\]

\[x_{1} = \frac{1 + 5}{12} = \frac{1}{2} = 0,5;\]

\[x_{2} = \frac{1 - 5}{12} = - \frac{4}{12} = - \frac{1}{3}.\]

\[6\left( x + \frac{1}{3} \right)(x - 0,5) < 0\]

\[x \in \left( - \frac{1}{3};0,5 \right).\]