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МатематикаРешебник по алгебре 9 класс Макарычев Задание 315
Задание 315
\[\boxed{\text{315\ (315).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[\textbf{а)}\ 7x^{2} - 10x + 7 > 0 \Longrightarrow\]
\[\Longrightarrow парабола,\ ветви\ вверх.\]
\[D = 25 - 7 \cdot 7 = - 24 < 0 \Longrightarrow\]
\[\Longrightarrow нет\ пересечения\ с\ осью\ \text{Ox}.\]
\[\Longrightarrow 7x^{2} - 10x + 7 > 0 \Longrightarrow\]
\[\Longrightarrow при\ любом\ x.\]
\[\textbf{б)} - 6y^{2} + 11y - 10 < 0 \Longrightarrow\]
\[\Longrightarrow парабола,\ ветви\ вниз.\]
\[D = 121 - 4 \cdot 6 \cdot 10 =\]
\[= - 119 < 0 \Longrightarrow нет\ пересечения\ \]
\[с\ осью\ \text{Ox}.\]
\[\Longrightarrow - 6y^{2} + 11y - 10 < 0 \Longrightarrow\]
\[\Longrightarrow при\ любом\ y.\]
\[\textbf{в)}\ 4x^{2} + 12x + 9 \geq 0\]
\[(2x + 3)^{2} \geq 0 \Longrightarrow верно\ при\ \]
\[любом\ x.\]
\[\textbf{г)}\frac{1}{4}x^{2} - 8x + 64 \geq 0\]
\[\left( \frac{1}{2}x - 8 \right)^{2} \geq 0 \Longrightarrow верно\ при\ \]
\[любом\ x.\]
\[\textbf{д)} - 9y^{2} + 6y - 1 \leq 0\]
\[9y^{2} - 6y + 1 \geq 0\]
\[(3y - 1)^{2} \geq 0 \Longrightarrow верно\ при\ \]
\[любом\ y.\]
\[\textbf{е)} - 5x^{2} + 8x - 5 < 0\]
\[5x^{2} - 8x + 5 > 0 \Longrightarrow парабола,\ \]
\[ветви\ вверх,\ найдем\ \]
\[пересечение\ с\ \text{Ox}:\]
\[D = 16 - 5 \cdot 5 = - 9 < 0 \Longrightarrow\]
\[\Longrightarrow нет\ пересечения\ с\ осью\ \text{Ox}.\]
\[\Longrightarrow - 5x^{2} + 8x - 5 < 0 \Longrightarrow\]
\[\Longrightarrow при\ любом\ x.\]
\[\boxed{\text{315.}\text{\ }\text{ОК\ ГДЗ\ -\ домашка\ на\ 5}}\]
\[\textbf{а)}\ x^{5} - x^{3} = 0\]
\[x^{3}\left( x^{2} - 1 \right) = 0\]
\[x^{3}(x - 1)(x + 1) = 0\]
\[x_{1} = 0;\ \ x_{2} = 1;\ \ x_{3} = - 1.\]
\[Ответ:x = 0;x = \pm 1.\]
\[\textbf{б)}\ x^{6} = 4x^{4}\]
\[x^{6} - 4x^{4} = 0\]
\[x^{4} \cdot \left( x^{2} - 4 \right) = 0\]
\[x^{4} \cdot (x - 2)(x + 2) = 0\]
\[x_{1} = 0;\ \ x_{2} = 2;\ \ x_{3} = - 2.\]
\[Ответ:x = 0;\ \ x = \pm 2.\]
\[\textbf{в)}\ 0,5x^{3} = 32x\ \ \ \ | \cdot 2\]
\[x^{3} = 64x\]
\[x^{3} - 64x = 0\]
\[x\left( x^{2} - 64 \right) = 0\]
\[x(x - 8)(x + 8) = 0\]
\[x_{1} = 0;\ \ x_{2} = 8;\ \ x_{3} = - 8.\]
\[Ответ:x = 0;\ \ x = \pm 8.\]
\[\textbf{г)}\ 0,2x^{4} = 4x^{2}\ \ \ \ \ \ \ \ | \cdot 5\]
\[x^{4} = 20x^{2}\]
\[x^{4} - 20x^{2} = 0\]
\[x^{2}\left( x^{2} - 20 \right) = 0\]
\[x^{2}\left( x - \sqrt{20} \right)\left( x + \sqrt{20} \right) = 0\]
\[x_{1} = 0;\ \ x_{2} = \sqrt{20} = 2\sqrt{5};\ \]
\[\ x_{3} = - 2\sqrt{5}.\]
\[Ответ:x = 0;\ \ x = \pm 2\sqrt{5}.\]
