Question

\(\sqrt{\frac{\sqrt{5}-2}{\sqrt{5}+1}}+\sqrt{\frac{\sqrt{5}+2}{5\sqrt{5}+11}}\)

Answer 1

Bằng 1,204609992 nhé

Answer 2

= 1,204609992

Answer 3

\(=\sqrt{\frac{\left(\sqrt{5}-2\right)\left(\sqrt{5}-1\right)}{\left(\sqrt{5}+1\right)\left(\sqrt{5}-1\right)}}+\sqrt{\frac{\left(\sqrt{5}-2\right)\left(5\sqrt{5}-11\right)}{\left(5\sqrt{5}+11\right)\left(5\sqrt{5}-11\right)}}\)

\(=\sqrt{\frac{7-3\sqrt{5}}{4}}+\sqrt{\frac{3-\sqrt{5}}{4}}\)

\(=\frac{\sqrt{7-3\sqrt{5}}+\sqrt{3-\sqrt{5}}}{2}\)

\(=\frac{\sqrt{14-6\sqrt{5}}+\sqrt{6-2\sqrt{5}}}{2\sqrt{2}}\)

\(=\frac{\sqrt{\left(3-\sqrt{5}\right)^2}+\sqrt{\left(\sqrt{5}-1\right)^2}}{2\sqrt{2}}=\frac{3-\sqrt{5}+\sqrt{5}-1}{2\sqrt{2}}=\frac{2}{2\sqrt{2}}=\frac{1}{\sqrt{2}}\)