ГДЗ по алгебре 8 класс Макарычев ФГОС Задание 1009

\[\boxed{\text{1009.\ }\text{еуроки}\text{-}\text{ответы}\text{\ }\text{на}\text{\ }\text{пятёрку}}\]

\[\left( \sqrt{(a + c)(b + d)} \right)^{2} \geq\]

\[\geq \left( \sqrt{\text{ab}} + \sqrt{\text{cd}} \right)^{2}\]

\[(a + c)(b + d) \geq ab +\]

\[+ 2\sqrt{\text{abcd}} + cd\]

\[(a + c)(b + d) \geq 2\sqrt{\text{abcd}} +\]

\[+ 2\sqrt{\text{abcd}}\]

\[(a + c)(b + d) \geq 4\sqrt{\text{abcd}}\]

\[a + c \geq 2\sqrt{\text{ac}},\]

\[\ \ b + d = 2\sqrt{\text{bd}} \Longrightarrow\]

\[\Longrightarrow (a + c)(b + d) =\]

\[= 2\sqrt{\text{ac}} \cdot 2\sqrt{\text{bd}}\]

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

\[= 4\sqrt{\text{abcd}} \Longrightarrow ч.т.д.\]