GIẢI
\(M=\frac{\sqrt[2]{4-\sqrt{5+\sqrt{20+1+2\sqrt{20.1}}}}}{\sqrt{10}-\sqrt{2}}=\frac{\sqrt[2]{4-\sqrt{5+\sqrt{\left(\sqrt{20}+1\right)^2}}}}{\sqrt{10}-\sqrt{2}}\)
\(=\frac{\sqrt[2]{4-\sqrt{5+\sqrt{20}+1}}}{\sqrt{10}-\sqrt{2}}=\frac{\sqrt[2]{4-\sqrt{5+1+2\sqrt{5}}}}{\sqrt{10}-\sqrt{2}}\)
\(=\frac{\sqrt[2]{4-\sqrt{\left(\sqrt{5}+1\right)^2}}}{\sqrt{10}-\sqrt{2}}=\frac{\sqrt[2]{4-\left(\sqrt{5}+1\right)}}{\sqrt{2}\left(\sqrt{5}-1\right)}=\frac{\sqrt{2}.\sqrt{3-\sqrt{5}}}{\sqrt{5}-1}\)
\(=\frac{\sqrt{6-2\sqrt{5}}}{\sqrt{5}-1}=\frac{\sqrt{5+1-2\sqrt{5}}}{\sqrt{5}-1}=\frac{\sqrt{\left(\sqrt{5}-1\right)^2}}{\sqrt{5}-1}=\frac{\sqrt{5}-1}{\sqrt{5}-1}=1\)
Chúc bạn học tốt !!!
