\(F=\sqrt{x+2\sqrt{2x-4}}+\sqrt{x-2\sqrt{2x-4}};\left(x\ge2\right)\)
\(\Rightarrow\sqrt{2}.F=\sqrt{2x+4\sqrt{2x-4}}+\sqrt{2x-4\sqrt{2x-4}}\)
\(\Leftrightarrow\sqrt{2}.F=\sqrt{\left(\sqrt{2x-4}+2\right)^2}+\sqrt{\left(\sqrt{2x-4}-2\right)^2}\)
\(\Leftrightarrow\sqrt{2}.F=\left|\sqrt{2x-4}+2\right|+ \left|\sqrt{2x-4}-2\right|\)
`@` TH1: \(2\le x< 4\)
\(\Leftrightarrow\sqrt{2}.F=\sqrt{2x-4}+2-\sqrt{2x-4}+2\)
\(\Leftrightarrow\sqrt{2}.F=4\)
\(\Leftrightarrow F=2\sqrt{2}\)
`@` TH2: \(x\ge4\)
\(\Leftrightarrow\sqrt{2}.F=\sqrt{2x-4}+2+\sqrt{2x-4}-2\)
\(\Leftrightarrow\sqrt{2}.F=2\sqrt{2x-4}\)
\(\Leftrightarrow F=2\sqrt{x-2}\)
Vậy \(2\le x< 4\) thì \(F=2\sqrt{2}\)
\(x\ge4\) thì \(F=2\sqrt{x-2}\)
