1) \(\sqrt{2x+1}=\sqrt{x}\left(đk:x\ge0\right)\)
\(\Leftrightarrow2x+1=x\Leftrightarrow x=-1\left(ktm\right)\)
Vậy \(S=\varnothing\)
2) \(\sqrt{4x-3}=\sqrt{x+2}\left(đk:x\ge\dfrac{3}{4}\right)\)
\(\Leftrightarrow4x-3=x+2\)
\(\Leftrightarrow3x=5\Leftrightarrow x=\dfrac{5}{3}\left(tm\right)\)
3) \(\sqrt{4\left(x+2\right)^2}=8\)
\(\Leftrightarrow2\left|x+2\right|=8\)
\(\Leftrightarrow\left|x+2\right|=4\)
\(\Leftrightarrow\left[{}\begin{matrix}x+2=4\\x+2=-4\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-6\end{matrix}\right.\)
4) \(\sqrt{x-2-3}.\sqrt{x^2-4}=0\left(đk:x\ge5\right)\)
\(\Leftrightarrow\sqrt{\left(x-5\right)\left(x-2\right)\left(x+2\right)}=0\)
\(\Leftrightarrow\left(x-5\right)\left(x-2\right)\left(x+2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=5\left(tm\right)\\x=2\left(ktm\right)\\x=-2\left(ktm\right)\end{matrix}\right.\)
