√(3+√(5-√(13+√48)))+√(1-√(5-√(13+√48)))=

Решите задачу:

$\sqrt{3+ \sqrt{5- \sqrt{13+ \sqrt{48} } } } + \sqrt{1- \sqrt{5- \sqrt{13+ \sqrt{48} } } } =\\ \\ \\ = \sqrt{3+ \sqrt{5- \sqrt{( \sqrt{12}+1)^2 } } } + \sqrt{1- \sqrt{5- \sqrt{( \sqrt{12}+1)^2 } } } =\\ \\ \\ = \sqrt{3+ \sqrt{5- \sqrt{12}-1 } } + \sqrt{1- \sqrt{5- \sqrt{12}-1 } } =\\ \\ \\ = \sqrt{3+ \sqrt{4- \sqrt{12} } } + \sqrt{1- \sqrt{4- \sqrt{12} } } =\\ \\ \\ = \sqrt{3+ \sqrt{ (\sqrt{3}-1)^2 } } + \sqrt{1-( \sqrt{3}-1)^2 } =\\ \\ \\ = \sqrt{3+ \sqrt{3}-1 } + \sqrt{1-\sqrt{3}+1} =$ $=\sqrt{2+\sqrt{3}}+\sqrt{2-\sqrt{3}}=\sqrt{(\sqrt{1.5}+\sqrt{0.5})^2}+\sqrt{(\sqrt{1.5}-\sqrt{0.5})^2}=\\ \\ \\ =|\sqrt{1.5}+\sqrt{0.5}|+|\sqrt{1.5}-\sqrt{0.5}|=\sqrt{1.5}+\sqrt{0.5}+\sqrt{1.5}-\sqrt{0.5}= \sqrt{6}$