Lời giải:
\(M=\frac{2\sqrt{4-\sqrt{5+\sqrt{20+1+2\sqrt{20.1}}}}}{\sqrt{10}-\sqrt{2}}=\frac{2\sqrt{4-\sqrt{5+\sqrt{(\sqrt{20}+1)^2}}}}{\sqrt{10}-\sqrt{2}}\)
\(=\frac{2\sqrt{4-\sqrt{5+\sqrt{20}+1}}}{\sqrt{10}-\sqrt{2}}=\frac{2\sqrt{4-\sqrt{5+1+2\sqrt{5}}}}{\sqrt{10}-\sqrt{2}}\)
\(=\frac{2\sqrt{4-\sqrt{(\sqrt{5}+1)^2}}}{\sqrt{10}-\sqrt{2}}=\frac{2\sqrt{4-(\sqrt{5}+1)}}{\sqrt{2}(\sqrt{5}-1)}=\frac{\sqrt{2}.\sqrt{3-\sqrt{5}}}{\sqrt{5}-1}\)
\(=\frac{\sqrt{6-2\sqrt{5}}}{\sqrt{5}-1}=\frac{\sqrt{5+1-2\sqrt{5}}}{\sqrt{5}-1}=\frac{\sqrt{(\sqrt{5}-1)^2}}{\sqrt{5}-1}=\frac{\sqrt{5}-1}{\sqrt{5}-1}=1\)
Lời giải:
\(M=\frac{2\sqrt{4-\sqrt{5+\sqrt{20+1+2\sqrt{20.1}}}}}{\sqrt{10}-\sqrt{2}}=\frac{2\sqrt{4-\sqrt{5+\sqrt{(\sqrt{20}+1)^2}}}}{\sqrt{10}-\sqrt{2}}\)
\(=\frac{2\sqrt{4-\sqrt{5+\sqrt{20}+1}}}{\sqrt{10}-\sqrt{2}}=\frac{2\sqrt{4-\sqrt{5+1+2\sqrt{5}}}}{\sqrt{10}-\sqrt{2}}\)
\(=\frac{2\sqrt{4-\sqrt{(\sqrt{5}+1)^2}}}{\sqrt{10}-\sqrt{2}}=\frac{2\sqrt{4-(\sqrt{5}+1)}}{\sqrt{2}(\sqrt{5}-1)}=\frac{\sqrt{2}.\sqrt{3-\sqrt{5}}}{\sqrt{5}-1}\)
\(=\frac{\sqrt{6-2\sqrt{5}}}{\sqrt{5}-1}=\frac{\sqrt{5+1-2\sqrt{5}}}{\sqrt{5}-1}=\frac{\sqrt{(\sqrt{5}-1)^2}}{\sqrt{5}-1}=\frac{\sqrt{5}-1}{\sqrt{5}-1}=1\)