ГДЗ по алгебре 8 класс Макарычев ФГОС Задание 710

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\[\textbf{а)}\ \left\{ \begin{matrix} x^{2} + y^{2} + 3xy = - 1 \\ x + 2y = 0\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} x = - 2y\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 4y^{2} + y^{2} + 3y \cdot ( - 2y) = - 1 \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} x = - 2y \\ y^{2} = 1\ \ \ \ \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} y_{1} = 1\ \ \ \\ x_{1} = - 2 \\ \end{matrix} \right.\ \text{\ \ \ }или\ \text{\ \ \ }\left\{ \begin{matrix} y_{2} = - 1 \\ x_{2} = 2\ \ \ . \\ \end{matrix} \right.\ \]

\[Ответ:\ ( - 2;1);(2;\ - 1).\]

\[\textbf{б)}\ \left\{ \begin{matrix} u + 2v = 4\ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ u^{2} + uv - v = - 5 \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} u = 4 - 2v\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 16 - 16v + 4v^{2} + 4v - 2v^{2} - v = - 5 \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} u = 4 - 2v\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 2v^{2} - 13v + 21 = 0 \\ \end{matrix} \right.\ \]

\[2v^{2} - 13v + 21 = 0\]

\[D = 169 - 4 \cdot 2 \cdot 21 = 1\]

\[v_{1} = \frac{13 - 1}{4} = 3;\ \ \ \]

\[v_{2} = \frac{13 + 1}{4} = 3,5.\]

\[1)\ \left\{ \begin{matrix} v_{1} = 3\ \ \ \ \\ u_{1} = - 2 \\ \end{matrix} \right.\ ;\ \ \ 2)\ \left\{ \begin{matrix} v_{2} = 3,5\ \\ u_{2} = - 3. \\ \end{matrix} \right.\ \]

\[Ответ:\ ( - 2;3);( - 3;3,5).\]