Решебник по алгебре 9 класс Мерзляк Задание 430

\[\boxed{\text{430\ (430).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[1)\ 5x^{2} - 7|x| + 2 \geq 0\]

\[\left\{ \begin{matrix} 5x^{2} - 7x + 2 \geq 0 \\ 5x^{2} + 7x + 2 \geq 0 \\ \end{matrix} \right.\ \]

\[1)\ 5x^{2} - 7x + 2 \geq 0\]

\[D = 49 - 40 = 9\]

\[x_{1,2} = \frac{7 \pm 3}{10}\]

\[x = 0,4;\ \ \ x = 1\]

\[2)\ 5x^{2} + 7x + 2 \geq 0\]

\[D = 49 - 40 = 9\]

\[x_{1,2} = \frac{- 7 \pm 3}{10}\]

\[x = 0,4;\ \ \ x = - 1\]

\[Ответ:x \in ( - \infty; - 1\rbrack \cup\]

\[\cup \lbrack - 0,4;0,4\rbrack \cup \lbrack 1; + \infty).\]

\[2)\ x^{2} + 10|x| - 24 \leq 0\]

\[\left\{ \begin{matrix} x^{2} + 10x - 24 \leq 0 \\ x^{2} - 10x - 24 \leq 0 \\ \end{matrix} \right.\ \]

\[1)\ x^{2} + 10x - 24 \leq 0\]

\(x_{1} + x_{2} = - 10,\ \ \ \ \ \ \ \ \ \ \ x_{1} = - 12\)

\[x_{1}x_{2} = - 24,\ \ x_{2} = 2\]

\[2)\ x^{2} - 10x - 24 \leq 0\]

\(x_{1} + x_{2} = 10,\ \ \ \ \ \ \ \ \ \ \ x_{1} = 12\)

\[x_{1}x_{2} = - 24,\ \ x_{2} = - 2\]

\[Ответ:x \in \lbrack - 2;2\rbrack.\]