Question

Rút gọn: \(A=\sqrt{x+2\sqrt{2x-4}}+\sqrt{x-2\sqrt{2x-4}}\)

Answer 1

\(A=\sqrt{x+2\sqrt{2x-4}}+\sqrt{x-2\sqrt{2x-4}}=\sqrt{x-2+2\sqrt{2}.\sqrt{x-2}+2}+\sqrt{x-2-2\sqrt{2}.\sqrt{x-2}+2}=\text{| }\sqrt{x-2}+\sqrt{2}\text{| }+\text{| }\sqrt{x-2}-\sqrt{2}\text{| }\) +) \(A=\sqrt{x-2}+\sqrt{2}+\sqrt{x-2}-\sqrt{2}=2\sqrt{x-2}\left(\text{ }\sqrt{x-2}\text{≥}\sqrt{2}\right)\)

+) \(A=\sqrt{x-2}+\sqrt{2}+\sqrt{2}-\sqrt{x-2}=2\sqrt{2}\left(\sqrt{x-2}< \sqrt{2}\right)\)