Question

\(\sqrt{4-\sqrt{5}}\)\(-\)\(\sqrt{4+\sqrt{5}}\)

Answer 1

\(A=\sqrt{4-\sqrt{5}}-\sqrt{4+\sqrt{5}}\)

\(\Rightarrow A^2=4-\sqrt{5}+4+\sqrt{5}-2\sqrt{\left(4-\sqrt{5}\right)\left(4+\sqrt{5}\right)}=8-2\sqrt{11}\)

\(\Rightarrow A=\sqrt{8-2\sqrt{11}}\)

Đề lỗi chăng?

Answer 2

Sửa đề: \(\sqrt{4-\sqrt{15}}-\sqrt{4+\sqrt{15}}\)

\(=\dfrac{\sqrt{8-2\sqrt{15}}-\sqrt{8+2\sqrt{15}}}{\sqrt{2}}\)

\(=\dfrac{\sqrt{5}-\sqrt{3}-\sqrt{5}-\sqrt{3}}{\sqrt{2}}\)

\(=-\sqrt{6}\)