Đáp án + giải thích các bước giải:
`(3-\sqrt{5})\sqrt{3+\sqrt{5}}+(3+\sqrt{5})\sqrt{3-\sqrt{5}}`
`=\sqrt{3-\sqrt{5}}.\sqrt{3-\sqrt{5}}.\sqrt{3+\sqrt{5}}+\sqrt{3+\sqrt{5}}.\sqrt{3+\sqrt{5}}.\sqrt{3-\sqrt{5}}`
`=\sqrt{3-\sqrt{5}}.\sqrt{3+\sqrt{5}}(\sqrt{3-\sqrt{5}}+\sqrt{3+\sqrt{5}})`
`=\sqrt{(3-\sqrt{5})(3+\sqrt{5})}(\sqrt{3-\sqrt{5}}+\sqrt{3+\sqrt{5}})`
`=\sqrt{9-5}(\sqrt{3-\sqrt{5}}+\sqrt{3+\sqrt{5}})`
`=2(\sqrt{3-\sqrt{5}}+\sqrt{3+\sqrt{5}})`
`=\sqrt{2}(\sqrt{2}.\sqrt{3-\sqrt{5}}+\sqrt{2}.\sqrt{3+\sqrt{5}})`
`=\sqrt{2}(\sqrt{6-2\sqrt{5}}+\sqrt{6+2\sqrt{5}})`
`=\sqrt{2}(\sqrt{5-2\sqrt{5}+1}+\sqrt{5+2\sqrt{5}+1})`
`=\sqrt{2}(\sqrt{(\sqrt{5}-1)^2+\sqrt{(\sqrt{5}+1)^2})`
`=\sqrt{2}(|\sqrt{5}-1|+|\sqrt{5}+1|)`
`=\sqrt{2}(\sqrt{5}-1+\sqrt{5}+1)`
`=\sqrt{2}.2\sqrt{5}`
`=2\sqrt{10}`
