Question

Rút gọn biểu thức

A=\(\sqrt{x+2\sqrt{2x-4}}+\sqrt{x-2\sqrt{2x-4}}\)

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

Answer 1

\(A=\sqrt{x+2\sqrt{2x-4}}+\sqrt{x-2\sqrt{2x-4}}=\sqrt{x+2.\sqrt{2}.\sqrt{x-2}}+\sqrt{x-2.\sqrt{2}.\sqrt{x-2}}=\sqrt{x-2+2.\sqrt{2}.\sqrt{x-2}+2}+\sqrt{x-2-2.\sqrt{2}.\sqrt{x-2}+2}=\sqrt{\left(\sqrt{x-2}+\sqrt{2}\right)^2}+\sqrt{\left(\sqrt{x-2}-\sqrt{2}\right)^2}=\text{|}\sqrt{x-2}+\sqrt{2}\text{|}+\text{|}\sqrt{x-2}-\sqrt{2}\text{|}=2\sqrt{x-2}\)\(B^2=\left(\sqrt{x+\sqrt{2x-1}}+\sqrt{x-\sqrt{2x-1}}\right)^2=2x+2\sqrt{\left(x+\sqrt{2x-1}\right)\left(x-\sqrt{2x-1}\right)}=2x+2\sqrt{\left(x^2-\left(2x-1\right)^2\right)}\left(ban-tu-tinh-not-nhe\right)\)