a) \(\sqrt{2x-1}\ge\sqrt{x+1}\) (ĐK: \(x\ge\dfrac{1}{2}\))
\(\Leftrightarrow2x-1\ge x+1\)
\(\Leftrightarrow2x-x\ge1+1\)
\(\Leftrightarrow x\ge2\left(tm\right)\)
b) \(\sqrt{2x}\le\sqrt{x^2}\) (ĐK: \(x\ge0\))
\(\Leftrightarrow2x\le x^2\)
\(\Leftrightarrow2x-x^2\le0\)
\(\Leftrightarrow x\left(2-x\right)\le0\)
\(\Leftrightarrow\left[{}\begin{matrix}\left[{}\begin{matrix}x\le0\\2-x\ge0\end{matrix}\right.\\\left[{}\begin{matrix}x\ge0\\2-x\le0\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left[{}\begin{matrix}x\le0\\x\le2\end{matrix}\right.\\\left[{}\begin{matrix}x\ge0\\x\ge2\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x\le0\left(ktm\right)\\x\ge2\end{matrix}\right.\)
\(\Leftrightarrow x\ge2\)
a: =>2x-1>=x+1
=>x>=2
b: =>2x<=x^2 và x>=0
=>x^2-2x>=0 và x>=0
=>x>=2
