Решебник по алгебре 9 класс Мерзляк Задание 620

 

\[\boxed{\mathbf{620\ (620).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[\left( |x| + 1 \right)\left( x^{2} + 5x - 6 \right) > 0,\]

\[\text{\ \ }|x| + 1 - всегда > 0.\]

\[\left\{ \begin{matrix} |x| + 1 > 0\ \ \ \ \ \ \ \ \ \\ x^{2} + 5x - 6 > 0 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} |x| > - 1\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ (x + 6)(x - 1) > 0 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ }\]

\[\ \left\{ \begin{matrix} x - любое\ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ (x + 6)(x - 1) > 0 \\ \end{matrix} \right.\ \]

\[x^{2} + 5x - 6 = 0\]

\[x_{1} + x_{2} = - 5,\ \ x_{1} = - 6\]

\[x_{1}x_{2} = - 6,\ \ x_{2} = 1\]

\[Ответ:x \in ( - \infty;\ - 6) \cup\]

\[(1;\ + \infty).\]

\[\boxed{\mathbf{620.\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[12;24;36;\ldots\]

\[\ d = 24 - 12 = 12\]

\[a_{1} + d(n - 1) < 200\]

\[12 + 12 \cdot (n - 1) < 200\]

\[12 + 12n - 12 < 200\]

\[12n < 200\]

\[n < 16,7\]

\[n = 16\]

\[S_{16} = \frac{2a_{1} + 15d}{2} \cdot 16 =\]

\[= (2 \cdot 12 + 15 \cdot 12) \cdot 8 =\]

\[= 204 \cdot 8 = 1632.\]

\[Ответ:1632.\]