Найдите значение выражения:
1) $\frac{5}{4 - 3\sqrt{2}} - \frac{5}{4 + 3\sqrt{2}}$;
2) $\frac{1}{\sqrt{4 + \sqrt{15}} + 1} - \frac{1}{\sqrt{4 + \sqrt{15}} - 1}$;
3) $(\sqrt{5 - 2\sqrt{6}} + \sqrt{5 + 2\sqrt{6}})^2$.
$\frac{5}{4 - 3\sqrt{2}} - \frac{5}{4 + 3\sqrt{2}} = \frac{5(4 + 3\sqrt{2}) - 5(4 - 3\sqrt{2})}{(4 - 3\sqrt{2})(4 + 3\sqrt{2})} = \frac{20 + 15\sqrt{2} - 20 + 15\sqrt{2}}{4^2 - (3\sqrt{2})^2} = \frac{30\sqrt{2}}{16 - 9 * 2} = \frac{30\sqrt{2}}{16 - 18} = \frac{30\sqrt{2}}{-2} = -15\sqrt{2}$
$\frac{1}{\sqrt{4 + \sqrt{15}} + 1} - \frac{1}{\sqrt{4 + \sqrt{15}} - 1} = \frac{\sqrt{4 + \sqrt{15}} - 1 - (\sqrt{4 + \sqrt{15}} + 1)}{(\sqrt{4 + \sqrt{15}} + 1)(\sqrt{4 + \sqrt{15}} - 1)} = \frac{\sqrt{4 + \sqrt{15}} - 1 - \sqrt{4 + \sqrt{15}} - 1}{(\sqrt{4 + \sqrt{15}})^2 - 1^2} = \frac{-2}{4 + \sqrt{15} - 1} = \frac{-2}{3 + \sqrt{15}} = \frac{-2(3 - \sqrt{15})}{(3 + \sqrt{15})(3 - \sqrt{15})} = \frac{-2(3 - \sqrt{15})}{3^2 - (\sqrt{15})^2} = \frac{-2(3 - \sqrt{15})}{9 - (\sqrt{15})^2} = \frac{-2(3 - \sqrt{15})}{9 - 15} = \frac{-2(3 - \sqrt{15})}{-6} = \frac{3 - \sqrt{15}}{3}$
$(\sqrt{5 - 2\sqrt{6}} + \sqrt{5 + 2\sqrt{6}})^2 = (\sqrt{5 - 2\sqrt{6}})^2 + 2 * \sqrt{5 - 2\sqrt{6}} * \sqrt{5 + 2\sqrt{6}} + (\sqrt{5 + 2\sqrt{6}})^2 = 5 - 2\sqrt{6} + 2(5^2 - (2\sqrt{6})^2) + 5 + 2\sqrt{6} = 10 + 2(25 - 4 * 6) = 10 + 2(25 - 24) = 10 + 2 * 1 = 12$
Пожауйста, оцените решение
