Решебник по алгебре 8 класс Мерзляк ФГОС Задание 780

 

\[\boxed{\mathbf{780\ (780).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[\left\{ \begin{matrix} (3x - 1)^{2} = t\ \ \ \ \ \ \ \ \\ t^{2} - 20t + 64 = 0 \\ \end{matrix} \right.\ \]

\[t_{1} + t_{2} = 20,\ \ t_{1} \cdot t_{2} = 64,\ \]

\[\ t_{1} = 4,\ \ t_{2} = 16\]

\[Ответ:\ x = \pm 1;\ x = - \frac{1}{3};x = \ \frac{5}{3}.\]

\[\left\{ \begin{matrix} (2x + 3)^{2} = t\ \ \ \ \ \ \ \ \\ t² - 24t - 25 = 0 \\ \end{matrix} \right.\ \]

\[t_{1} + t_{2} = 24,\ \ t_{1} \cdot t_{2} = - 25,\ \]

\[\ t_{1} = - 1,\ \ t_{2} = 25\]

\[Ответ:\ x = - 4;x = 1.\]

\[\boxed{\mathbf{7}\mathbf{8}\mathbf{0}\mathbf{\text{.\ }}Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ x_{1}² + x_{2}² = 12\]

\[\left( x_{1} + x_{2} \right)^{2} - 2x_{1}x_{2} = 12\]

\[x^{2} - 4x + a = 0\]

\[x_{1} + x_{2} = 4\]

\[x_{1}x_{2} = a\]

\[4^{2} - 2a = 12\]

\[2a = 4\]

\[a = 2\]

\[Ответ:при\ a = 2.\]

\[2)\ x_{1}² + x_{2}² = 6\]

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

\[x_{1} + x_{2} = 4\]

\[x_{1}x_{2} = a\]

\[4² - 2a = 6\]

\[2a = 10\]

\[a = 5 - не\ подходит.\]

\[Ответ:таких\ \text{a\ }\ нет.\]