Question

Tìm giá trị bieeru thức

\(A=\left(2\sqrt{4+\sqrt{6-2\sqrt{5}}}\right)\left(\sqrt{10}-\sqrt{2}\right)\)

Answer 1

A = \(\left(2\sqrt{4+\sqrt{6-2\sqrt{5}}}\right)\left(\sqrt{10}-\sqrt{2}\right)\)

A = \(\left(2\sqrt{4+\sqrt{\left(\sqrt{5}-1\right)^2}}\right)\left(\sqrt{10}-\sqrt{2}\right)\)

A = \(\left(2\sqrt{3+\sqrt{5}}\right)\left(\sqrt{5}-1\right)\sqrt{2}\)

A = \(\sqrt{2}\sqrt{6+2\sqrt{5}}\left(\sqrt{5}-1\right)\sqrt{2}\)

A = \(\sqrt{2}\sqrt{\left(\sqrt{5}+1\right)^2}\left(\sqrt{5}-1\right)\sqrt{2}\)

A = \(\left(\sqrt{5}+1\right)\left(\sqrt{5}-1\right)\sqrt{2}\sqrt{2}\)

A = \(\left(5-1\right)2\) = \(8\)