Алгебра
Английский
Биология
География
Геометрия
История
Русский
Обществознание
Физика
Химия
Информатика
Литература
МатематикаРешебник по алгебре 9 класс Мерзляк Задание 763
Задание 763
\[\boxed{\mathbf{763\ (763).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]
\[a_{1} = 9;\ \ a_{7} = 15\]
\[S_{n} = \frac{a_{1} + a_{n}}{2} \cdot n\ \ \]
\[S_{7} = \frac{a_{1} + a_{7}}{2} \cdot 7 = \frac{9 + 15}{2} \cdot 7 =\]
\[= 12 \cdot 7 = 84.\]
\[\boxed{\mathbf{763.\ }Еуроки\ - \ ДЗ\ без\ мороки}\]
\[1)\ \left| x^{2} - 2x - 6 \right| = 6\]
\[x^{2} - 2x - 6 = 6\]
\[x^{2} - 2x - 12 = 0\]
\[D_{1} = 1 + 12 = 13\]
\[x = 1 \pm \sqrt{13}.\]
\[x^{2} - 2x - 6 = - 6\]
\[x^{2} - 2x = 0\]
\[x(x - 2) = 0\]
\[x = 0;\ \ x = 2.\]
\[Ответ:\ \ 0;\ \ 2;\ \ 1 \pm \sqrt{13}.\]
\[2)\ x^{2} - 6|x| - 16 = 0\]
\[x^{2} - 6x - 16 = 0\]
\[D_{1} = 9 + 16 = 25\]
\[x_{1} = 3 + 5 = 8;\]
\[x_{2} = 3 - 5 = - 2.\]
\[x^{2} + 6x - 16 = 0\]
\[D_{1} = 9 + 16 = 25\]
\[x_{1} = - 3 + 5 = 2;\]
\[x_{2} = - 3 - 5 = - 8.\]
\[Ответ:\ \pm 2;\ \pm 8.\]
\[3)\ x|x| + 2x - 15 = 0\]
\[x^{2} + 2x - 15 = 0\]
\[D_{1} = 1 + 15 = 16\]
\[x_{1} = - 1 + 4 = 3;\]
\[x_{2} = - 1 - 4 = - 5.\]
\[- x^{2} + 2x - 15 = 0\]
\[x^{2} - 2x + 15 = 0\]
\[D_{1} = 1 - 15 < 0\]
\[нет\ корней.\]
\[Ответ:\ - 5;\ \ 3.\]
\[4)\ \left| \left| x^{2} - 6x - 4 \right| - 3 \right| = 1\]
\[\left| x^{2} - 6x - 4 \right| - 3 = 1\]
\[\left| x^{2} - 6x - 4 \right| = 4\]
\[x^{2} - 6x - 4 = 4\]
\[x^{2} - 6x - 8 = 0\]
\[D_{1} = 9 + 8 = 17\]
\[x = 3 \pm \sqrt{17}.\]
\[x^{2} - 6x - 4 = - 4\]
\[x^{2} - 6x = 0\]
\[x(x - 6) = 0\]
\[x = 0;\ \ x = 6.\]
\[\left| x^{2} - 6x - 4 \right| - 3 = - 1\]
\[\left| x^{2} - 6x - 4 \right| = 2\]
\[x^{2} - 6x - 4 = 2\]
\[x^{2} - 6x - 6 = 0\]
\[D_{1} = 9 + 6 = 15\]
\[x = 3 \pm \sqrt{15}.\]
\[x^{2} - 6x - 4 = - 2\]
\[x^{2} - 6x - 2 = 0\]
\[D_{1} = 9 + 2 = 11\]
\[x = 3 \pm \sqrt{11}.\]
\[Ответ:3 \pm \sqrt{11};\ \ 3 \pm \sqrt{15};\ \ \]
\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 3 \pm \sqrt{17};\ \ 0;6.\]
