Question

rút gọn

a,\(\sqrt{x-2\sqrt{x-1}}\)+\(\sqrt{x+2\sqrt{x-1}}\)

b,\(\sqrt{5-2\sqrt{6}}\)+\(\sqrt{5+2\sqrt{6}}\)

 

Answer 1

\(a,\sqrt{x-2\sqrt{x-1}}+\sqrt{x+2\sqrt{x-1}}\left(Đk:x\ge1\right)\)

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

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

\(=|\sqrt{x-1}-1|+|\sqrt{x-1}+1|\)

\(=\sqrt{x-1}-1+\sqrt{x-1}+1=2\sqrt{x-1}\)(Ko chắc:v)

\(b,\sqrt{5-2\sqrt{6}}+\sqrt{5+2\sqrt{6}}\)

\(=\sqrt{\left(\sqrt{2}-\sqrt{3}\right)^2}+\sqrt{\left(\sqrt{2}+\sqrt{3}\right)^2}\)

\(=|\sqrt{2}-\sqrt{3}|+|\sqrt{2}+\sqrt{3}|\)

\(=\sqrt{3}-\sqrt{2}+\sqrt{2}+\sqrt{3}=2\sqrt{3}\)