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МатематикаРешебник по алгебре 9 класс Мерзляк Задание 429
Задание 429
\[\boxed{\text{429\ (429).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[1)\text{\ x}^{2} - 8|x| - 33 < 0\]
\[\left\lbrack \begin{matrix} x^{2} - 8x - 33 < 0 \\ x^{2} + 8x - 33 < 0 \\ \end{matrix} \right.\ \]
\[1)\ x^{2} - 8x - 33 < 0\]
\(x_{1} + x_{2} = 8,\ \ \ \ \ \ \ \ \ \ \ x_{1} = - 3\)
\[x_{1}x_{2} = - 33,\ \ x_{2} = 11\]
\[2)\ x^{2} + 8x - 33 < 0\]
\(x_{1} + x_{2} = - 8,\ \ \ \ \ \ \ \ \ \ \ x_{1} = - 11\)
\[x_{1}x_{2} = - 33,\ \ x_{2} = 3\]
\[Ответ:x \in ( - 11;11).\]
\[2)\ 8x^{2} + 7|x| - 1 \geq 0\]
\[\left\lbrack \begin{matrix} 8x^{2} + 7x - 1 \geq 0 \\ 8x^{2} - 7x - 1 \geq 0 \\ \end{matrix} \right.\ \]
\[1)\ 8x^{2} + 7x - 1 \geq 0\]
\[D = 49 + 32 = 81\]
\[x_{1,2} = \frac{- 7 \pm 9}{16}\]
\[x = - 1;\ \ \ x = \frac{1}{8}\]
\[2)\ 8x^{2} - 7x - 1 \geq 0\]
\[D = 49 + 32 = 81\]
\[x_{1,2} = \frac{7 \pm 9}{16}\]
\[x = 1;\ \ x = - \frac{1}{8}\]
\[Ответ:x \in \left( - \infty;\ - \frac{1}{8} \right\rbrack \cup \left\lbrack \frac{1}{8}; + \infty \right).\]
\[\boxed{\text{429.\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[1)\ y = x^{2} + 2x - 8\]
\[x_{0} = \frac{- 2}{2} = - 1;\]
\[y_{0} = 1 - 2 - 8 = - 9.\]
\[\text{Ox}:\ \ \]
\[x^{2} + 2x - 8 = 0\]
\[x_{1} + x_{2} = - 2,\ \ x_{1} = - 4,\ \ \]
\[( - 4;0)\]
\[x_{1}x_{2} = - 8,\ \ x_{2} = 2,\ \ \]
\[(2;0).\]
\[Oy:\ \ \]
\[y = - 8;\ \ x = 0,\ \ (0; - 8)\]
\[y( - 3) = 9 - 6 - 8 = - 5.\]
\[2)\ y = x^{2} - 2x\]
\[x_{0} = \frac{2}{2} = 1;\]
\[y_{0} = 1 - 2 = - 1.\]
\[Ox:\]
\[x^{2} - 2x = 0\]
\[x(x - 2) = 0,\ \ \]
\[x = 0,\ \ x = 2,\ \ \]
\[(0;0),\ \ (2;0).\]
\[Oy:\ \ \]
\[y = 0;\ (0;0).\]
\[y( - 1) = 1 + 2 = 3.\]
\[3)\ y = - x^{2} + 4x - 5\]
\[x_{0} = \frac{- 4}{- 2} = 2;\ \]
\[y_{0} = - 4 + 8 - 5 = - 1.\]
\[Ox:\ \ \ \]
\[- x^{2} + 4x - 5 = 0\]
\[D = 16 - 20 < 0 - \ точек\ нет.\]
\[Oy:\ \ \ \]
\[y = - 5;\ \ \ (0;\ - 5).\]
\[y(1) = - 1 + 4 - 5 = - 2.\]
\[4)\ y = 2x^{2} - 2x - 4\]
\[x_{0} = \frac{2}{4} = 0,5\]
\[y_{0} = 0,5 - 1 - 4 = - 4,5\]
\[\text{Ox}:\ \ 2x^{2} - 2x - 4 = 0\ \ |\ :2\]
\[x^{2} - x - 2 = 0\]
\[x_{1} + x_{2} = 1,\ \ x_{1}x_{2} = - 2,\ \ \]
\[x_{1} = 2,\ \ x_{2} = - 1.\]
\[(2;0),\ \ ( - 1;0).\]
\[\text{Oy}:\ \ \]
\[\ y = - 4,\ \ (0; - 4).\]
