Решебник по алгебре 9 класс Макарычев Задание 309

 

\[\boxed{\text{309\ (309).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[\textbf{а)}\ 0,01x^{2} \leq 1\ \ \ \ \ \ | \cdot 100\]

\[x^{2} \leq 100\]

\[x^{2} - 100 \leq 0\]

\[(x - 10)(x + 10) \leq 0\]

\[x \in \lbrack - 10;10\rbrack.\]

\[\textbf{б)}\frac{1}{2}x^{2} > 12\ \ \ \ \ \ | \cdot 2\]

\[x^{2} > 24\ \]

\[x^{2} - 24 > 0\]

\[\left( x - 2\sqrt{6} \right)\left( x + 2\sqrt{6} \right) > 0\]

\[x \in \left( - \infty;\ - 2\sqrt{6} \right) \cup \left( 2\sqrt{6}; + \infty \right).\]

\[\textbf{в)}\ 4x \leq - x^{2}\]

\[x^{2} + 4x \leq 0\]

\[x(x + 4) \leq 0\]

\[x \in \lbrack - 4;0\rbrack.\]

\[\textbf{г)}\ \ \frac{1}{3}x^{2} > \frac{1}{9}\ \ \ \ \ \ \ | \cdot 3\]

\[x^{2} > \frac{1}{3}\]

\[x^{2} - \frac{1}{3} > 0\]

\[\left( x - \sqrt{\frac{1}{3}} \right)\left( x + \sqrt{\frac{1}{3}} \right) > 0\]

\[x \in \left( - \infty;\ - \frac{\sqrt{3}}{3} \right) \cup \left( \frac{\sqrt{3}}{3}; + \infty \right).\]

\[\textbf{д)}\ 5x^{2} > 2x\]

\[5x^{2} - 2x > 0\]

\[5x(x - 0,4) > 0\]

\[x \in ( - \infty;0) \cup (0,4; + \infty).\]

\[\textbf{е)} - 0,3x < 0,6x^{2}\]

\[0,6x^{2} + 0,3x > 0\]

\[0,6x(x + 0,5) > 0\]

\[x \in ( - \infty;\ - 0,5) \cup (0; + \infty).\]

\[\boxed{\text{309.}\text{\ }\text{ОК\ ГДЗ\ -\ домашка\ на\ 5}}\]

\[1)\ x³ - x + 3 = 0 \Longrightarrow среди\ \]

\[делителей\ 3\ нет\ целых\ корней;\]

\[2)\ x^{4} + x² - 20 = 0\]

\[\left( x^{2} - 4 \right)\left( x^{2} + 5 \right) = 0\]

\[x_{1,2} = \pm 2;\]

\[3)\ x^{4} + 5x² + 4 = 0\]

\[\left( x^{2} + 1 \right)\left( x^{2} + 4 \right) = 0 \Longrightarrow\]

\[\Longrightarrow корней\ нет;\]

\[4)\ x³ - 5x + 4 = 0\]

\[(x - 1)\left( x^{2} + x - 4 \right) = 0\]

\[D = 1 + 16 = 17\]

\[\Longrightarrow целый\ корень\ только\ \]

\[один:\ \ x = 1.\]

\[Ответ:\ \ 4).\]