Question

\(\sqrt{9+2\sqrt{5}}\) -\(\sqrt{9-2\sqrt{5}}\)

Answer 1

bạn thêm cho mjk chút xíu phần cuối đến rồi:

Mà \(\sqrt{9+2\sqrt{5}}>\sqrt{9-2\sqrt{5}}\text{ nên }A>0\text{ nên }A=\sqrt{18-2\sqrt{61}}\)

Answer 2

\(\text{Đặt }A=\sqrt{9+2\sqrt{5}}-\sqrt{9-2\sqrt{5}}\)

\(\Rightarrow A^2=\left(\sqrt{9+2\sqrt{5}}-\sqrt{9-2\sqrt{5}}\right)\)

\(=9+2\sqrt{5}-2\sqrt{9+2\sqrt{5}}\sqrt{9-2\sqrt{5}}+9-2\sqrt{5}\)

\(=18-2\sqrt{\left(9+2\sqrt{5}\right)\left(9-2\sqrt{5}\right)}\)

\(=18-2\sqrt{81-20}\)

\(=18-2\sqrt{61}\)

\(\Rightarrow A=\sqrt{18-2\sqrt{61}}\text{ hoặc }A=-\sqrt{18-2\sqrt{61}}\)