Question

Rút gọn bài này giúp mk vs ạ m.n.:

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

mk đaq cần gấp ạ tks trước!

Answer 1

điều kiện : \(x\ge1\)

ta có : \(P=\sqrt{x+2\sqrt{x-1}}+\sqrt{x-2\sqrt{x-1}}\)

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

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

\(\Rightarrow\left[{}\begin{matrix}P=2\sqrt{x-1}\left(x\ge2\right)\\P=2\left(1\le x< 2\right)\end{matrix}\right.\)

vậy .....................................................................................................