Решебник по алгебре 9 класс Мерзляк Задание 756

\[\boxed{\mathbf{756\ (756).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[Запишем:\ \]

\[\ \frac{1}{a + c} = \frac{\frac{1}{b + c} + \frac{1}{a + b}}{2}\text{\ \ }\]

\[\frac{2}{a + c} = \frac{1}{b + c} + \frac{1}{a + b}\]

\[\frac{2}{a + c} = \frac{a + b + b + c}{(b + c)(a + b)}\text{\ \ }\]

\[\frac{2}{a + c} = \frac{a + c + 2b}{(b + c)(a + b)}\text{\ \ }\]

\[\frac{2}{a + c} = \frac{a + c + 2b}{ab + b^{2} + ac + bc}\ \]

\[2 \cdot \left( ab + b^{2} + ac + bc \right) =\]

\[= (a + c)(a + c + 2b)\]

\[2ab + 2b^{2} + 2ac + 2bc =\]

\[= a^{2} + ac + 2ab + ac +\]

\[+ c^{2} + 2bc\]

\[2b^{2} = a^{2} + c^{2}\ или\ \ \ \ \]

\[b^{2} = \frac{a^{2} + c^{2}}{2}\text{\ \ }\]

\[Тогда:\ \ \]

\[a^{2},\ b^{2},\ c^{2} - тоже\ члены\]

\[\ арифметической\ прогрессии.\]