Question

Помогите с алгеброй пожалуйста, задание во вложениях

Answer 1

$\sqrt{9-2 \sqrt{20} } + \sqrt{14-3 \sqrt{20} } = \sqrt{9-4 \sqrt{5} } + \sqrt{14-6 \sqrt{5} } = \\\ = \sqrt{2^2-2\cdot2 \sqrt{5}+ (\sqrt{5})^2} + \sqrt{3^2-2\cdot3 \sqrt{5} +(\sqrt{5})^2} = \\\ = \sqrt{(2-\sqrt{5})^2} + \sqrt{(3-\sqrt{5})^2} =|2-\sqrt{5}| + |3-\sqrt{5}|= \\\ =\sqrt{5}-2 + 3-\sqrt{5}=1$

$\sqrt{19-2 \sqrt{48} } - \sqrt{7- \sqrt{48} } = \sqrt{19-8 \sqrt{3} } - \sqrt{7- 4\sqrt{3} } = \\\ = \sqrt{4^2-2\cdot4 \sqrt{3}+ (\sqrt{3})^2} - \sqrt{2^2-2\cdot2 \sqrt{3} +(\sqrt{3})^2} = \\\ = \sqrt{(4-\sqrt{3})^2} - \sqrt{(2-\sqrt{3})^2} =|4-\sqrt{3}| - |2-\sqrt{3}|= \\\ =4-\sqrt{3}-(2-\sqrt{3})=4-\sqrt{3}-2+\sqrt{3}=2$