Question

Rút gọn:

\(A=\sqrt{3-\sqrt{5}}.\left(\sqrt{10}-\sqrt{2}\right)\left(3+\sqrt{5}\right)\)

\(B=\sqrt{x+2\sqrt{x-1}}+\sqrt{x+2\sqrt{x-1}}\)

Answer 1

\(A=\sqrt{3-\sqrt{5}}\left(\sqrt{10}-\sqrt{2}\right)\left(3+\sqrt{5}\right)=\sqrt{3-\sqrt{5}}.\sqrt{2}\left(\sqrt{5}-1\right)\left(3+\sqrt{5}\right)=\sqrt{5-2\sqrt{5}+1}\left(3+\sqrt{5}\right)\left(\sqrt{5}-1\right)=\left(\sqrt{5}-1\right)^2\left(3+\sqrt{5}\right)=2\left(3-\sqrt{5}\right)\left(3+\sqrt{5}\right)=2\left(9-5\right)=8\)

\(B=\sqrt{x-2\sqrt{x-1}}+\sqrt{x+2\sqrt{x-1}}=\sqrt{x-1-2\sqrt{x-1}+1}+\sqrt{x-1+2\sqrt{x-1}+1}=|\sqrt{x-1}-1|+\left|\sqrt{x-1}+1\right|\left(x\ge1\right)\)