Решебник по алгебре 9 класс Макарычев Задание 708

 

\[\boxed{\text{708\ (708).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[\textbf{а)}\ a_{2} \cdot a_{6} = a_{3} \cdot a_{5};\]

\[a_{2} \cdot a_{6} = a_{1}q \cdot a_{1}q^{5} = a_{1}^{2} \cdot q^{6},\]

\[a_{3} \cdot a_{5} = a_{1}q² \cdot a_{1}q^{4} = a_{1}^{2}{\cdot q}^{6},\]

\[a_{2} \cdot a_{6} = a_{3} \cdot a_{5} \Longrightarrow ч.т.д.\]

\[\textbf{б)}\ a_{n - 3} \cdot a_{n + 8} = a_{n} \cdot a_{n + 5},\]

\[где\ n > 3,\]

\[\ a_{n - 3} \cdot a_{n + 8} = a_{1}q^{n - 4} \cdot a_{1}q^{n + 7} =\]

\[= a_{1}^{2}q^{2n + 3},\]

\[a_{n} \cdot a_{n + 5} = a_{1}q^{n - 1} \cdot a_{1}q^{n + 4} =\]

\[= a_{1}^{2}q^{2n + 3},\]

\[a_{n - 3} \cdot a_{n + 8} = a_{n} \cdot a_{n + 5} \Longrightarrow ч.т.д.\]

\[\boxed{\text{708.}\text{\ }\text{ОК\ ГДЗ\ -\ домашка\ на\ 5}}\]

\[\textbf{а)}\ \frac{ab^{2} - 16a}{5b^{3}} \cdot \frac{20b^{5}}{a^{2}b + 4a^{2}} =\]

\[= \frac{a(b - 4)(b + 4)}{5b^{3}} \cdot \frac{20b^{5}}{a^{2}(b + 4)} =\]

\[= \frac{4b^{2}(b - 4)}{a} = \frac{4b³ - 16b²}{2}\]

\[\textbf{б)}\ \frac{7xy}{x^{2} - 4xy + 4y^{2}} \cdot \frac{3x - 6y}{14y^{2}} =\]

\[= \frac{7xy}{(x - 2y)^{2}} \cdot \frac{3(x - 2y)}{14y^{2}} =\]

\[= \frac{3x}{(x - 2y) \cdot 2y} = \frac{3x}{2xy - 4y²}\]

\[\textbf{в)}\ \frac{p^{3} - 125}{8p^{2}} \cdot \frac{4p}{p^{2} + 5p + 25} =\]

\[= \frac{p - 5}{2p}\]

\[\textbf{г)}\ \frac{9m^{2} - 12mn + 4n^{2}}{3m^{3} + 24n^{3}} \cdot \frac{3m + 6n}{2n - 3m} =\]

\[= \frac{2n - 3m}{m² - 2mn + 4n²}\]