a: ĐKXĐ: \(\left\{{}\begin{matrix}x+6>=0\\x-2>=0\end{matrix}\right.\Leftrightarrow x>=2\)
\(\sqrt{x+6}-\sqrt{x-2}=2\)
=>\(\left(\sqrt{x+6}-\sqrt{x-2}\right)^2=4\)
=>\(x+6+x-2-2\sqrt{\left(x+6\right)\left(x-2\right)}=4\)
=>\(2\sqrt{\left(x+6\right)\left(x-2\right)}=2x+4-4=2x\)
=>\(\sqrt{\left(x+6\right)\left(x-2\right)}=x\)
=>\(\left\{{}\begin{matrix}x>=0\\\left(x+6\right)\left(x-2\right)=x^2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x>=2\\x^2+4x-12=x^2\end{matrix}\right.\)
=>x=3
b: ĐKXĐ: \(x-3>=0\)
=>x>=3
\(2\sqrt{x-3}-2x+3=0\)
=>\(\sqrt{4x-12}=2x-3\)
=>\(\left\{{}\begin{matrix}x>=\dfrac{3}{2}\\4x-12=4x^2-12x+9\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x>=3\\4x^2-12x+9-4x+12=0\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x>=3\\4x^2-16x+21=0\end{matrix}\right.\Leftrightarrow x\in\varnothing\)
