Решебник по алгебре 8 класс Макарычев ФГОС Задание 1308

\[\boxed{\text{1308.\ }\text{еуроки}\text{-}\text{ответы}\text{\ }\text{на}\text{\ }\text{пятёрку}}\]

\[\left\{ \begin{matrix} a + c = 2b\ \ \ \ \ \ \ \ \\ 2bd = c(b + d) \\ \end{matrix} \right.\ ,\ \ b \neq 0,\]

\[\ \ d \neq 0\]

\[(1)\frac{a}{b} = \frac{c}{d} - доказать.\]

\[\left\{ \begin{matrix} a = 2b - c \\ c = \frac{2bd}{b + d}\text{\ \ } \\ \end{matrix} \right.\ \text{\ \ \ \ }\]

\[Подставим\ в\ (1).\]

\[\frac{2b - c}{b} = \frac{\frac{2bd}{b + d}}{d}\]

\[\frac{2b - c}{b} = \frac{2bd}{d(b + d)}\]

\[\frac{2b - c}{b} = \frac{2b}{b + d}\]

\[(2b - c)(b + d) = 2b^{2}\]

\[2b^{2} + 2bd - cb - cd = 2b^{2}\]

\[2bd - cb - cd = 0\]

\(2bd - c(b + d) = 0\)

\[2bd = c(b + d) \Longrightarrow ч.т.д.\]