Ta có \(2\sqrt{4+\sqrt{6-2\sqrt{5}}}\left(\sqrt{10}-\sqrt{2}\right)\)
= \(2\sqrt{4+\sqrt{\sqrt{5}^2-2\sqrt{5}.1+1}}\sqrt{2}\left(\sqrt{5}-1\right)\)
= \(2\sqrt{4+\sqrt{\left(\sqrt{5}-1\right)^2}}\sqrt{2}\left(\sqrt{5}-1\right)\)
= \(\sqrt{2}\sqrt{4+\sqrt{5}-1}.\left(\sqrt{5}-1\right)2\)
= \(\sqrt{2\left(3+\sqrt{5}\right)}\left(\sqrt{5}-1\right)2\)
= \(\sqrt{6+2\sqrt{5}}\left(\sqrt{5}-1\right)2\)
= \(\sqrt{\left(\sqrt{5}+1\right)^2}\left(\sqrt{5}-1\right)2\)
= \(\left(\sqrt{5}+1\right)\left(\sqrt{5}-1\right)2\)
= \(\left(\sqrt{5}^2-1\right)2\)
= 4.2
= 8
Chúc bạn làm bài tốt :)
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