ГДЗ по алгебре 9 класс Макарычев Задание 219

 

\[\boxed{\text{219}\text{\ (219)}\text{.}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[\left\{ \begin{matrix} \alpha \cdot \beta = 4\ \ \ \ \ \ \ \ \ \\ \sqrt{\alpha} + \sqrt{\beta} = 3 \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} \alpha \cdot \beta = 4\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \left( \sqrt{\alpha} + \sqrt{\beta} \right)^{2} = 3^{2} \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} \alpha \cdot \beta = 4\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \alpha + 2\sqrt{\text{αβ}} + \beta = 9 \\ \end{matrix} \right.\ \Longrightarrow\]

\[\left\{ \begin{matrix} \alpha\beta = 4\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \alpha + 2 \cdot 2 + \beta = 9 \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} \alpha\beta = 4\ \ \ \ \ \ \\ \alpha + \beta = 5 \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\lbrack \begin{matrix} \left\{ \begin{matrix} \alpha = 1 \\ \beta = 4 \\ \end{matrix} \right.\ \\ \left\{ \begin{matrix} \alpha = 4 \\ \beta = 1 \\ \end{matrix} \right.\ \\ \end{matrix} \right.\ .\]

\[\boxed{\text{219.}\text{\ }\text{ОК\ ГДЗ\ -\ домашка\ на\ 5}}\]

\[\textbf{а)}\ x³ + 7x² - 6 = 0\]

\[x_{1} = - 1 \Longrightarrow корень\ уравнения\ \]

\[(методом\ подбора);\]

\[\Longrightarrow x^{3} + 7x^{2} - 6 =\]

\[= (x + 1)\left( x^{2} + 6x - 6 \right)\]

\[(x + 1)\left( x^{2} + 6x - 6 \right) = 0\]

\[x_{1} = - 1\]

\[x^{2} + 6x - 6 = 0\]

\[D = 9 + 6 = 15\]

\[x_{2,3} = - 3 \pm \sqrt{15}.\]

\[Ответ:x = - 1;x - 3 \pm \sqrt{15}.\]

\[\textbf{б)}\ x³ + 4x² - 5 = 0\]

\[x_{1} = 1 \Longrightarrow корень\ уравнения\]

\[\ (методом\ подбора);\]

\[\Longrightarrow x^{3} + 4x^{2} - 5 =\]

\[= (x - 1)\left( x^{2} + 5x + 5 \right)\]

\[(x - 1)\left( x^{2} + 5x + 5 \right) = 0\]

\[x_{1} = 1\]

\[x^{2} + 5x + 5 = 0\]

\[D = 25 - 4 \cdot 5 = 25 - 20 = 5\]

\[x_{2,3} = \frac{- 5 \pm \sqrt{5}}{2}\]

\[Ответ:x = 1;\ \ x = \frac{- 5 \pm \sqrt{5}}{2}.\]