Đáp án:
$\sqrt{\dfrac{3+\sqrt{5}}{2}}+\sqrt{\dfrac{7-3\sqrt{5}}{2}}=2$
Giải thích các bước giải:
$\sqrt{\dfrac{3+\sqrt{5}}{2}}+\sqrt{\dfrac{7-3\sqrt{5}}{2}}\\=\sqrt{\dfrac{6+2\sqrt{5}}{4}}+\sqrt{\dfrac{14-6\sqrt{5}}{4}}\\=\sqrt{\dfrac{6+2.1.\sqrt{5}}{4}}+\sqrt{\dfrac{14-2.3.\sqrt{5}}{4}}\\=\sqrt{\dfrac{(\sqrt{5}+1)^2}{4}}+\sqrt{\dfrac{(3-\sqrt{5})^2}{4}}\\=\dfrac{|\sqrt{5}+1|}{2}+\dfrac{|3-\sqrt{5}|}{2}\\=\dfrac{\sqrt{5}+1}{2}+\dfrac{3-\sqrt{5}}{2}\,\,\,(\sqrt{5}+1>0; 3-\sqrt{5}>0)\\=\dfrac{\sqrt{5}+1+3-\sqrt{5}}{2}\\=\dfrac{4}{2}\\=2$
