Решебник по алгебре 8 класс Мерзляк ФГОС Задание 712

 

\[\boxed{\mathbf{712\ (712).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ x² + bx + c = 0\]

\[x_{1} = - 2\]

\[x_{2} = 0,5\]

\[x_{1} + x_{2} = - b = - 2 + 0,5 = - 1,5,\ \ \]

\[b = 1,5\]

\[x_{1} \cdot x_{2} = c = - 2 \cdot 0,5 = - 1,\ \ \]

\[c = - 1\]

\[Ответ:b = 1,5;\ \ c = - 1.\]

\[2)x² + bx + c = 0\ \]

\[x_{1} = - 10\]

\[x_{2} = - 20\]

\[x_{1} + x_{2} = - b = - 10 - 20 =\]

\[= - 30,\ \ b = 30\]

\[x_{1} \cdot x_{2} = c = - 10 \cdot ( - 20) = 200,\ \ \]

\[c = 200\]

\[Ответ:\ b = 30;\ \ c = 200.\]

\[\boxed{\mathbf{71}\mathbf{2}\mathbf{\text{.\ }}Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ \left\{ \begin{matrix} y^{2} - x = 14 \\ x - y = - 2\ \ \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} x = y - 2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ y^{2} - (y - 2) = 14 \\ \end{matrix} \right.\ \]

\[y^{2} - y + 2 - 14 = 0\]

\[y^{2} - y - 12 = 0\]

\[y_{1} + y_{2} = 1;\ \ \ y_{1} \cdot y_{2} = - 12\]

\[y_{1} = - 3;\ \ \ \ y_{2} = 4.\]

\[x_{1} = y - 2 = - 3 - 2 = - 5;\]

\[x_{2} = y - 2 = 4 - 2 = 2.\]

\[Ответ:( - 5; - 3);(2;4).\]

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

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

\[1 - 3x - 2x^{2} = 2\]

\[2x^{2} + 3x + 1 = 0\]

\[D = 9 - 8 = 1\]

\[x_{1} = \frac{- 3 + 1}{4} = - \frac{2}{4} = - 0,5;\]

\[x_{2} = \frac{- 3 - 1}{4} = - 1;\]

\[y_{1} = 1 - 3x = 1 + 1,5 = 2,5;\]

\[y_{2} = 1 - 3x = 1 + 3 = 4.\]

\[Ответ:( - 0,5;2,5);( - 1;4).\]