ГДЗ по алгебре 8 класс Макарычев Задание 500

\[\boxed{\text{500\ (500).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[\textbf{а)}\ \frac{1^{\backslash 11 - 2\sqrt{30}}}{11 - 2\sqrt{30}} - \frac{1^{\backslash 11 + 2\sqrt{30}}}{11 + 2\sqrt{30}} =\]

\[= \frac{4\sqrt{30}}{121 - 4 \cdot 30} =\]

\[= \frac{4\sqrt{30}}{121 - 120} = 4\sqrt{30}\]

\[\textbf{б)}\ \frac{5^{\backslash 3 - 2\sqrt{2}}}{3 + 2\sqrt{2}} + \frac{5^{\backslash 3 + 2\sqrt{2}}}{3 - 2\sqrt{2}} =\]

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

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

\[= \frac{5 \cdot 6}{9 - 4 \cdot 2} = \frac{30}{9 - 8} = 30\]

\[= \frac{5 - 2\sqrt{15} + 3 + 5 + 2\sqrt{15} + 3}{5 - 3} =\]

\[= \frac{16}{2} = 8\]