Решебник по алгебре 9 класс Мерзляк Задание 414

\[\boxed{\text{414\ (414).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

Пояснение.

\[Решение\ квадратных\ \]

\[неравенств.\]

Решение.

\[1)\ x^{2} + 5x \leq 0\]

\[x(x + 5) \leq 0\]

\[x_{1} = 0,\ \ x_{2} = - 5\]

\[x \in \lbrack - 5;0\rbrack.\]

\[Ответ:\ x = - 5;\ - 4;\ - 3;\ \]

\[- 2;\ - 1;0.\]

\[2)\ x^{2} - 10 < 0\]

\[\left( x - \sqrt{10} \right)\left( x + \sqrt{10} \right) < 0\]

\[x_{1,2} = \pm \sqrt{10}\]

\[x \in \left( - \sqrt{10};\sqrt{10} \right).\]

\[Ответ:\ x = - 3;\ - 2;\ - 1;0;1;\]

\[2;3.\]

\[3)\ 6x^{2} + x - 2 \leq 0\]

\[D = 1 + 48 = 49\]

\[x_{1,2} = \frac{- 1 \pm 7}{12}\]

\[x = - \frac{2}{3};\ \ \ x = 0,5\]

\[x \in \left\lbrack - \frac{2}{3};0,5 \right\rbrack.\]

\[Ответ:x = 0.\]

\[4) - \frac{1}{4}x^{2} + x + 3 > 0\ | \cdot ( - 4)\]

\[x^{2} - 4x - 12 < 0\]

\[x_{1} + x_{2} = 4,\ \ x_{1} = 6\]

\[x_{1}x_{2} = - 12,\ \ x_{2} = - 2\]

\[x \in ( - 2;6).\]

\[Ответ:\ x = - 1;0;1;2;3;4;5.\ \]