\(A=\sqrt{x+2\sqrt{2x-4}}+\sqrt{x-2\sqrt{2x-4}}\)
\(\Leftrightarrow A^2=2x+2\sqrt{x^2-8x+16}=\)
\(=2x+\sqrt{\left(x-4\right)^2}\)
\(=2x+|x-4|\)
\(=\hept{\begin{cases}2x-x+4=x+4\left(2\le x< 4\right)\\2x+x-4=3x-4\left(x\ge4\right)\end{cases}}\)
\(\Rightarrow A=\hept{\begin{cases}\sqrt{x+4}\left(2\le x< 4\right)\\\sqrt{3x-4}\left(x\ge4\right)\end{cases}}\)
\(\sqrt{x+2\sqrt{2x-4}}+\sqrt{x-2\sqrt{2x-4}}=\)\(\frac{\sqrt{2}\left(\sqrt{x+2\sqrt{2x-4}}+\sqrt{x-2\sqrt{2x-4}}\right)}{\sqrt{2}}\)
\(=\frac{\sqrt{2}\left(\sqrt{x+2\sqrt{2x-4}}+\sqrt{x-2\sqrt{2x-4}}\right)}{\sqrt{2}}\)=\(\frac{\sqrt{2x+4\sqrt{2x-4}}+\sqrt{2x-4\sqrt{2x-4}}}{\sqrt{2}}\)
=\(\frac{\sqrt{2x-4+4\sqrt{2x-4}+4}+\sqrt{2x-4-4\sqrt{2x-4}+4}}{\sqrt{2}}\)=\(\frac{\sqrt{\left(\sqrt{2x-4}+2\right)^2}+\sqrt{\left(\sqrt{2x-4}-2\right)^2}}{\sqrt{2}}\)
còn lại tự làm nhá nhứ chia 2 trường hợp chúc em học rỏi
