\(\sqrt{x}-\sqrt{x-\sqrt{x}+\dfrac{1}{4}}\left(đk:x\ge0\right)\left(1\right)\)
\(=\sqrt{x}-\sqrt{\left(\sqrt{x}-\dfrac{1}{2}\right)^2}\)
\(=\sqrt{x}-\left|\sqrt{x}-\dfrac{1}{2}\right|\)
TH1: \(x\ge\dfrac{1}{4}\)
\(\left(1\right)=\sqrt{x}-\sqrt{x}+\dfrac{1}{2}=\dfrac{1}{2}\)
TH2: \(0\le x< \dfrac{1}{4}\)
\(\left(1\right)=\sqrt{x}+\sqrt{x}-\dfrac{1}{2}=2\sqrt{x}-\dfrac{1}{2}\)
\(=\sqrt{x}-\sqrt{\left(\sqrt{x}-\dfrac{1}{2}\right)^2}=\sqrt{x}-\left|\sqrt{x}-\dfrac{1}{2}\right|\)
\(=\left[{}\begin{matrix}\dfrac{1}{2}\text{ nếu }x\ge\dfrac{1}{4}\\2\sqrt{x}-\dfrac{1}{2}\text{ nếu }0\le x< \dfrac{1}{4}\end{matrix}\right.\)
