Question

[Đỗ Thị Minh Anh]

Thực hiện phép tính:

a) \(\sqrt{12-3\sqrt{7}}-\sqrt{12+3\sqrt{7}}\)

b) \(\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4-\sqrt{10+2\sqrt{5}}}\)

c) \(\sqrt{3-\sqrt{5}}+\sqrt{3+\sqrt{5}}\)

Answer 1

[Ngô Bá Hùng]

c)\(\sqrt{3-\sqrt{5}}+\sqrt{3+\sqrt{5}}=\sqrt{3+\sqrt{5}}+\sqrt{3-\sqrt{5}}=A\\ \Rightarrow\sqrt{2}A=\sqrt{6+2\sqrt{5}+}\sqrt{6-\sqrt{5}}=\sqrt{\left(\sqrt{5}+1\right)^2}+\sqrt{\left(\sqrt{5}-1\right)^2}\\ =\sqrt{5}+1+\sqrt{5}-1\\ =2\sqrt{5}\\ \Rightarrow A=\sqrt{2}.\sqrt{5}=\sqrt{10}\)