Решебник по алгебре 8 класс Мерзляк Задание 130

\[\boxed{\text{130\ (130).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

Пояснение.

Решение.

\[\frac{1^{\backslash 1 + a}}{1 - a} + \frac{1^{\backslash 1 - a}}{1 + a} + \frac{2}{1 + a^{2}} +\]

\[+ \frac{4}{1 + a^{4}} + \frac{8}{1 + a^{8}} + \frac{16}{1 + a^{16}} =\]

\[= \frac{32}{1 - a^{32}}\]

\[Упростим\ левую\ часть\ \]

\[равенства:\]

\[\frac{1 + a + 1 - a}{1 - a^{2}} + \frac{2}{1 + a^{2}} + \frac{4}{1 + a^{4}} +\]

\[+ \frac{8}{1 + a^{8}} + \frac{16}{1 + a^{16}} = \frac{32}{1 - a^{32}}\]

\[\frac{2^{\backslash 1 + a^{2}}}{1 - a^{2}} + \frac{2^{\backslash 1 - a^{2}}}{1 + a^{2}} + \frac{4}{1 + a^{4}} +\]

\[+ \frac{8}{1 + a^{8}} + \frac{16}{1 + a^{16}} = \frac{32}{1 - a^{32}}\]

\[\frac{4^{\backslash 1 + a^{4}}}{1 - a^{4}} + \frac{4^{\backslash 1 - a^{4}}}{1 + a^{4}} + \frac{8}{1 + a^{8}} +\]

\[+ \frac{16}{1 + a^{16}} = \frac{32}{1 - a^{32}}\]

\[\frac{8^{\backslash 1 + a^{8}}}{1 - a^{8}} + \frac{8^{\backslash 1 - a^{8}}}{1 + a^{8}} + \frac{16}{1 + a^{16}} =\]

\[= \frac{32}{1 - a^{32}}\]

\[\frac{16^{\backslash 1 + a^{16}}}{1 - a^{16}} + \frac{16^{\backslash 1 - a^{16}}}{1 + a^{16}} = \frac{32}{1 - a^{32}}\]

\[\frac{32}{1 - a^{32}} = \frac{32}{1 - a^{32}}\text{.\ }\]