Найдите значение выражения:
1) $(3\sqrt{2} + 1)(\sqrt{8} - 2)$;
2) $(3 - 2\sqrt{7})^2 + (3 + 2\sqrt{7})^2$;
3) $(10 - 4\sqrt{6})(2 + \sqrt{6})^2$;
4) $(\sqrt{9 - 4\sqrt{2}} + \sqrt{9 + 4\sqrt{2}})^2$.
$(3\sqrt{2} + 1)(\sqrt{8} - 2) = (3\sqrt{2} + 1)(\sqrt{4 * 2} - 2) = (3\sqrt{2} + 1)(2\sqrt{2} - 2) = 3\sqrt{2} * 2\sqrt{2} - 3\sqrt{2} * 2 + 1 * 2\sqrt{2} - 1 * 2 = 6 * 2 - 6\sqrt{2} + 2\sqrt{2} - 2 = 12 - 4\sqrt{2} - 2 = 10 - 4\sqrt{2}$
$(3 - 2\sqrt{7})^2 + (3 + 2\sqrt{7})^2 = 3^2 - 2 * 3 * 2\sqrt{7} + (2\sqrt{7})^2 + 3^2 + 2 * 3 * 2\sqrt{7} + (2\sqrt{7})^2 = 9 - 12\sqrt{7} + 4 * 7 + 9 + 12\sqrt{7} + 4 * 7 = 18 + 28 + 28 = 74$
$(10 - 4\sqrt{6})(2 + \sqrt{6})^2 = (10 - 4\sqrt{6})(2^2 + 2 * 2\sqrt{6} + (\sqrt{6})^2) = (10 - 4\sqrt{6})(4 + 4\sqrt{6} + 6) = (10 - 4\sqrt{6})(10 + 4\sqrt{6}) = 10^2 - (4\sqrt{6})^2 = 100 - 16 * 6 = 100 - 96 = 4$
$(\sqrt{9 - 4\sqrt{2}} + \sqrt{9 + 4\sqrt{2}})^2 = (\sqrt{9 - 4\sqrt{2}})^2 + 2\sqrt{9 - 4\sqrt{2}}\sqrt{9 + 4\sqrt{2}} + (\sqrt{9 + 4\sqrt{2}})^2 = 9 - 4\sqrt{2} + 2\sqrt{(9 - 4\sqrt{2})(9 + 4\sqrt{2})} + 9 + 4\sqrt{2} = 18 + 2\sqrt{9^2 - (4\sqrt{2})^2} = 18 + 2\sqrt{81 - 16 * 2} = 18 + 2\sqrt{81 - 32} = 18 + 2\sqrt{49} = 18 + 2 * 7 = 18 + 14 = 32$
Пожауйста, оцените решение
