ГДЗ по алгебре 9 класс Макарычев Задание 307

\[\boxed{\text{307\ (307).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[\textbf{а)}\ 2x^{2} + 5x + 3 > 0\]

\[2x^{2} + 5x + 3 = 0\]

\[D = 25 - 4 \cdot 2 \cdot 3 = 1\]

\[x_{1,2} = \frac{- 5 \pm 1}{4} = - 1,5;\ - 1;\]

\[2 \cdot (x + 1,5)(x + 1) > 0\]

\[x \in ( - \infty;\ - 1,5) \cup ( - 1; + \infty).\]

\[\textbf{б)} - x^{2} - \frac{1}{3}x - \frac{1}{36} < 0\]

\[x^{2} + \frac{1}{3}x + \frac{1}{36} > 0\ \ \ \ \ \ \ \ \ \ | \cdot 36\ \]

\[36x^{2} + 12x + 1 > 0\]

\[(6x + 1)^{2} > 0\]

\[36 \cdot \left( x + \frac{1}{6} \right)^{2} > 0\]

\[x \in \left( - \infty; - \frac{1}{6} \right) \cup \left( - \frac{1}{6}; + \infty \right).\]