Question

Rút gọn biểu thức

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

Answer 1

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

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

\(\Leftrightarrow\sqrt{x-1}=1\)

=>x-1=1

hay x=2

Answer 2

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

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

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

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

\(ĐK:x\ge1\)

\(\Leftrightarrow\sqrt{x-1}+1=2\) ( vì \(\sqrt{x-1}+1\ge1>0\) )

\(\Leftrightarrow\sqrt{x-1}=1\)

\(\Leftrightarrow x-1=1\)

\(\Leftrightarrow x=2\left(tm\right)\)

Vậy \(S=\left\{2\right\}\)