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МатематикаРешебник по алгебре 8 класс Мерзляк ФГОС Задание 711
Задание 711
\[\boxed{\mathbf{711\ (711).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]
\[1)\ x² + bx + c = 0\]
\[x_{1} = - 8\]
\[x_{2} = 6\]
\[x_{1} + x_{2} = - b = - 8 + 6 = - 2,\]
\[b = 2\]
\[x_{1} \cdot x_{2} = c = - 8 \cdot 6 = - 48,\ \ \]
\[c = - 48\]
\[Ответ:b = 2;\ \ c = - 48.\]
\[2)\ x² + bx + c = 0\]
\[x_{1} = 4\]
\[x_{2} = 5\]
\[x_{1} + x_{2} = - b = 4 + 5 = 9,\ \ \]
\[b = - 9\]
\(x_{1} \cdot x_{2} = c = 4 \cdot 5 = 20,\ \ c = 20\ \)
\[Ответ:b = - 9;\ \ c = 20.\]
\[\boxed{\mathbf{71}\mathbf{1}\mathbf{\text{.\ }}Еуроки\ - \ ДЗ\ без\ мороки}\]
\[1)\ \left\{ \begin{matrix} y = x + 3\ \ \ \ \ \\ x^{2} - 2y = 9 \\ \end{matrix} \right.\ \]
\[\left\{ \begin{matrix} y = x + 3\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ x^{2} - 2(x + 3) = 9 \\ \end{matrix} \right.\ \]
\[x^{2} - 2x - 6 - 9 = 0\]
\[x^{2} - 2x - 15 = 0\]
\[D_{1} = 1 + 15 = 16\]
\[x_{1} = 1 + 4 = 5;\]
\[y_{1} = x + 3 = 5 + 3 = 8;\]
\[x_{2} = 1 - 4 = - 3;\]
\[y_{2} = x + 3 = - 3 + 3 = 0.\]
\[Ответ:(5;8);( - 3;0).\]
\[2)\ \left\{ \begin{matrix} x + y = 5 \\ xy = 4\ \ \ \ \ \\ \end{matrix} \right.\ \]
\[\left\{ \begin{matrix} y = 5 - x\ \ \ \ \ \ \\ x(5 - x) = 4 \\ \end{matrix} \right.\ \]
\[5x - x^{2} = 4\]
\[x^{2} - 5x + 4 = 0\]
\[x_{1} + x_{2} = 5;\ \ \ x_{1} \cdot x_{2} = 4;\]
\[x_{1} = 1;\ \ \ \ \ x_{2} = 4;\]
\[y_{1} = 5 - x = 5 - 1 = 4;\]
\[y_{2} = 5 - x = 5 - 4 = 1.\]
\[Ответ:(1;4);(4;1).\]
\[3)\ \left\{ \begin{matrix} x - 4y = 2\ \ \ \\ xy + 2y = 8 \\ \end{matrix} \right.\ \text{\ \ }\]
\[\left\{ \begin{matrix} x = 4y + 2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ y(4y + 2) + 2y = 8 \\ \end{matrix} \right.\ \]
\[4y^{2} + 2y + 2y - 8 = 0\]
\[4y^{2} + 4y - 8 = 0\ \ \ |\ :4\]
\[y^{2} + y - 2 = 0\]
\[y_{1} + y_{2} = - 1;\ \ y_{1} \cdot y_{2} = - 2\]
\[y_{1} = - 2;\ \ \ \ y_{2} = 1;\]
\[x_{1} = 4y + 2 = - 8 + 2 = - 6;\]
\[x_{2} = 4y + 2 = 4 + 2 = 6.\]
\[Ответ:( - 6; - 2);(6;1).\]
\[4)\ \left\{ \begin{matrix} x^{2} + y^{2} = 8 \\ 3x + y = 4\ \\ \end{matrix} \right.\ \]
\[\left\{ \begin{matrix} y = 4 - 3x\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ x^{2} + (4 - 3x)^{2} = 8 \\ \end{matrix} \right.\ \]
\[x^{2} + 16 - 24x + 9x^{2} - 8 = 0\]
\[10x^{2} - 24x + 8 = 0\ \ \ |\ :2\]
\[5x^{2} - 12x + 4 = 0\]
\[D_{1} = 36 - 20 = 16\]
\[x_{1} = \frac{6 + 4}{5} = 2;\]
\[x_{2} = \frac{6 - 4}{5} = \frac{2}{5} = 0,4.\]
\[y_{1} = 4 - 3x = 4 - 6 = - 2;\]
\[y_{2} = 4 - 3x = 4 - 1,2 = 2,8.\]
\[Ответ:(2; - 2);(0,4;2,8).\]
