Решебник по алгебре 8 класс Мерзляк ФГОС Задание 1125

\[\boxed{\mathbf{1125}\mathbf{\text{.\ }}Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ \frac{5}{4 - 3\sqrt{2}} - \frac{5}{4 + 3\sqrt{2}} =\]

\[= \frac{5 \cdot \left( 4 + 3\sqrt{2} \right) - 5 \cdot \left( 4 - 3\sqrt{2} \right)}{\left( 4 - 3\sqrt{2} \right)\left( 4 + 3\sqrt{2} \right)} =\]

\[= \frac{20 + 15\sqrt{2} - 20 + 15\sqrt{2}}{16 - 9 \cdot 2} =\]

\[= \frac{30\sqrt{2}}{- 2} = - 15\sqrt{2}\]

\[2)\ \frac{1}{\sqrt{4 + \sqrt{15}} + 1} - \frac{1}{\sqrt{4 + \sqrt{15}} - 1} =\]

\[= \frac{\sqrt{4 + \sqrt{15}} - 1 - \sqrt{4 + \sqrt{15}} - 1}{\left( \sqrt{4 + \sqrt{15}} + 1 \right)\left( \sqrt{4 + \sqrt{15}} - 1 \right)} =\]

\[= \frac{- 2}{4 + \sqrt{15} - 1} = \frac{- 2}{3 + \sqrt{15}}\]

\[3)\ \left( \sqrt{5 - 2\sqrt{6}} + \sqrt{5 + 2\sqrt{6}} \right)^{2} =\]

\[= 5 - 2\sqrt{6} + 2\sqrt{\left( 5 - 2\sqrt{6} \right)\left( 5 + 2\sqrt{6} \right)} + 5 + 2\sqrt{6} =\]

\[= 10 + 2\sqrt{25 - 4 \cdot 6} =\]

\[= 10 + 2 \cdot 1 = 12\]