Решебник по алгебре 9 класс Мерзляк Задание 1034

\[\boxed{\mathbf{1034\ (1034).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[По\ т.\ Пифагора\ \ a^{2} +\]

\[+ (a + d)^{2} = (a + 2d)^{2}\]

\[a^{2} + a^{2} + 2ad + d^{2} - a^{2} -\]

\[- 4ad - 4d^{2} = 0\]

\[a² - 2ad - 3d^{2} = 0\ \ \ \ | \cdot ( - 1)\]

\[3d^{2} + 2ad - a^{2} = 0\]

\[D = 4a² + 12a² = 16a²\]

\[d = \frac{- 2a - 4a}{6} < 0\]

\[d = \frac{- 2a + 4a}{6} = \frac{a}{3}\]

\[a + d = a + \frac{a}{3} = \frac{4}{3}a\]

\[S = \frac{1}{2}a \cdot \frac{4}{3}a = \frac{4}{6}a² = \frac{2a^{2}}{3}\]

\[Ответ:\frac{2a^{2}}{3}.\]