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МатематикаРешебник по алгебре 9 класс Мерзляк Задание 806
Задание 806
\[\boxed{\mathbf{806\ (806).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]
\[1)\ 11 + 19 + 27 + \ldots +\]
\[+ (8n + 3) = 470\]
\[a_{1} = 11,\ \ d = 19 - 11 = 8,\ \]
\[\ a_{n} = 8n + 3,\ \ S_{n} = 470\]
\[S_{n} = \frac{a_{1} + a_{n}}{2} \cdot n\ \ \]
\[470 = \frac{11 + 8n + 3}{2} \cdot n\ \ \]
\[470 = \frac{8n + 14}{2} \cdot n\]
\[470 = (4n + 7) \cdot n\]
\[4n^{2} + 7n - 470 = 0,\ \ \]
\[D = 49 + 7520 = 7569\]
\[n = \frac{- 7 - 87}{8} < 0\ \ \]
\[n = \frac{- 7 + 87}{8} = 10\]
\[Ответ:n = 10.\]
\[2)\ 1 + 5 + 9 + \ldots + x = 630\]
\[a_{1} = 1,\ \ d = 5 - 1 = 4,\]
\[\text{\ \ }a_{n} = x,\ \ S_{n} = 630\]
\[S_{n} = \frac{2a_{1} + d(n - 1)}{2} \cdot n\ \ \]
\[630 = \frac{2 + 4 \cdot (n - 1)}{2} \cdot n\]
\[630 = \left( 1 + 2 \cdot (n - 1) \right) \cdot n\]
\[630 = (1 + 2n - 2) \cdot n\ \]
\[630 = (2n - 1) \cdot n\]
\[2n^{2} - n - 630 = 0\ \]
\[D = 1 + 5040 = 5041\]
\[n = \frac{1 - 71}{4} < 0\ \]
\[n = \frac{1 + 71}{4} = 18\]
\[a_{n} = a_{1} + d(n - 1) = x\ \ \]
\[x = 1 + 4 \cdot (18 - 1) =\]
\[= 1 + 4 \cdot 17 = 69\]
\[Ответ:x = 69.\]
\[\boxed{\mathbf{806.\ }Еуроки\ - \ ДЗ\ без\ мороки}\]
\[1)\ x² - 4x + 3 > 0\]
\[(x - 1)(x - 3) > 0\]
\[Ответ:x \in ( - \infty;1) \cup (3; + \infty).\]
\[2)\ x² - 6x - 40 \leq 0\]
\[(x - 10)(x + 4) \leq 0\]
\[Ответ:x \in \lbrack - 4;10\rbrack.\]
\[3)\ x² + x + 1 \geq 0\]
\[D = 1 - 4 < 0;\ \ ветви\ вверх;x - любое\ число.\]
\[Ответ:x \in ( - \infty; + \infty).\]
\[4)\ x² - x + 1 < 0\]
\[D = 1 - 4 < 0\]
\[Ответ:\ \varnothing.\]
\[5) - 3x^{2} + 2x + 1 > 0\]
\[- 3x^{2} + 2x + 1 = 0\]
\[D = 4 + 12 = 16\]
\[x_{1} = \frac{- 2 + 4}{- 6} = - \frac{1}{3}\]
\[x_{2} = \frac{- 2 - 4}{- 6} = 1\]
\[Ответ:x \in \left( - \frac{1}{3};1 \right).\]
\[6)\ x - x^{2} < 0\]
\[x(1 - x) < 0\]
\[Ответ:x \in ( - \infty;0) \cup (1;\ + \infty)\text{.\ }\]
\[7)\ x² + 25x \geq 0\]
\[x(x + 25) \geq 0\]
\[Ответ:x \in ( - \infty;\ - 25\rbrack \cup \lbrack 0; + \infty).\]
\[8)\ 0,1x² - 2 \leq 0\ \ \ | \cdot 10\]
\[x^{2} - 20 \leq 0\]
\[\left( x + 2\sqrt{5} \right)\left( x - 2\sqrt{5} \right) \leq 0\]
\[Ответ:x \in \left\lbrack - 2\sqrt{5};2\sqrt{5} \right\rbrack\text{.\ }\]
