ГДЗ по алгебре 8 класс Макарычев ФГОС Задание 852

\[\boxed{\text{852.\ }\text{еуроки}\text{-}\text{ответы}\text{\ }\text{на}\text{\ }\text{пятёрку}}\]

\[a,\ b > 0,\ \ a^{2} > b^{2} \Longrightarrow a > b\]

\[Доказательство:так\ как\ \]

\[a^{2} > b^{2} \Longrightarrow a^{2} - b^{2} > 0\]

\[(a - b)(a + b) > 0\]

\[так\ как\ \ a > 0,\ \ b > 0 \Longrightarrow\]

\[\Longrightarrow a + b > 0 \Longrightarrow (a - b) > 0 \Longrightarrow\]

\[\Longrightarrow a > b \Longrightarrow ч.т.д.\]

\[\textbf{а)}\ \left( \sqrt{6} + \sqrt{3} \right)^{2} - \left( \sqrt{7} + \sqrt{2} \right)^{2} > 0\]

\[6 + 2\sqrt{18} + 3 - 7 - 2\sqrt{14} -\]

\[- 2 > 0\]

\[2\sqrt{18} - 2\sqrt{14} > 0,\]

\[\ \ 2\sqrt{18} > 2\sqrt{14} \Longrightarrow\]

\[\Longrightarrow \sqrt{6} + \sqrt{3} > \sqrt{7} + \sqrt{2}\]

\[\textbf{б)}\ \left( \sqrt{3} + 2 \right)^{2} - \left( \sqrt{6} + 1 \right)^{2} > 0\]

\[3 + 4\sqrt{3} + 4 - 6 - 2\sqrt{6} - 1 > 0\]

\[4\sqrt{3} - 2\sqrt{6} > 0;\ \ 4\sqrt{3} > 2\sqrt{6} \Longrightarrow\]

\[\Longrightarrow \sqrt{3} + 2 > \sqrt{6} + 1\]

\[\textbf{в)}\ \left( \sqrt{5} - 2 \right)^{2} - \left( \sqrt{6} - \sqrt{3} \right)^{2} > 0\]

\[5 - 4\sqrt{5} + 4 - 6 + 2\sqrt{18} -\]

\[- 3 > 0\]

\[- 4\sqrt{5} + 2\sqrt{18} > 0;\ \]

\[\ 2\sqrt{18} > 4\sqrt{5} - неверно.\]

\[\Longrightarrow \sqrt{5} - 2 < \sqrt{6} - \sqrt{3}\]

\[\textbf{г)}\ \left( \sqrt{10} - \sqrt{7} \right)^{2} -\]

\[- \left( \sqrt{11} - \sqrt{6} \right)^{2} > 0\]

\[10 - 2\sqrt{70} + 7 - 11 +\]

\[+ 2\sqrt{66} - 6 > 0\]

\[- 2\sqrt{70} + 2\sqrt{66} > 0,\ \ \]

\[2\sqrt{66} > 2\sqrt{70} - неверно.\]

\[\Longrightarrow \sqrt{10} - \sqrt{7} > \sqrt{11} - \sqrt{6}\]