ĐKXĐ: \(a\ge2\)
Ta có: \(\sqrt{a+2\sqrt{2a-4}}-\sqrt{a-2\sqrt{2a-4}}\)
\(=\sqrt{a-2+2\cdot\sqrt{a-2}\cdot\sqrt{2}+2}-\sqrt{a-2-2\cdot\sqrt{a-2}\cdot\sqrt{2}+2}\)
\(=\sqrt{\left(\sqrt{a-2}+\sqrt{2}\right)^2}-\sqrt{\left(\sqrt{a-2}-\sqrt{2}\right)^2}\)
\(=\left|\sqrt{a-2}+\sqrt{2}\right|-\left|\sqrt{a-2}-\sqrt{2}\right|\)
\(=\sqrt{a-2}+\sqrt{2}-\left|\sqrt{a-2}-\sqrt{2}\right|\)(*)
Trường hợp 1: \(a\ge4\)
(*)\(=\sqrt{a-2}+\sqrt{2}-\left(\sqrt{a-2}-\sqrt{2}\right)\)
\(=\sqrt{a-2}+\sqrt{2}-\sqrt{a-2}+\sqrt{2}\)
\(=2\sqrt{2}\)
Trường hợp 2: a<4
(*)\(=\sqrt{a-2}+\sqrt{2}-\left(\sqrt{2}-\sqrt{a-2}\right)\)
\(=\sqrt{a-2}+\sqrt{2}-\sqrt{2}+\sqrt{a-2}\)
\(=2\sqrt{a-2}\)
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