\(b,\sqrt{x^2-4}-x^2+4=0\Leftrightarrow\sqrt{x^2-4}-\left(x^2-4\right)=0\Leftrightarrow\sqrt{x^2-4}=x^2-4.Dat:x^2-4=a\Rightarrow\sqrt{a}=a\Leftrightarrow a-\sqrt{a}=0\Leftrightarrow\sqrt{a}\left(\sqrt{a}-1\right)=0\Leftrightarrow\left[{}\begin{matrix}\sqrt{a}=0\\\sqrt{a}=1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}a=0\\a=1\end{matrix}\right.\) \(+,a=0\Rightarrow x^2-4=0\Leftrightarrow x^2=4\Leftrightarrow x=\pm2\)
\(+,a=1\Leftrightarrow x^2-4=1\Leftrightarrow x^2=5\Leftrightarrow x=\pm\sqrt{5}\)
\(c,\sqrt{2x-1}=x-3\Leftrightarrow2x-1=x^2-6x+9\Leftrightarrow x^2-8x+10=0\Leftrightarrow x^2-8x+16=6\Leftrightarrow\left(x-4\right)^2=6\Leftrightarrow x=\pm\sqrt{6}+4\)
b)\(\sqrt{x^2-4}-x^2+4\) =0
<=>\(\sqrt{x^2-4}\left(1-\sqrt{x^2-4}\right)\) =0
<=>\(\sqrt{x-2}.\sqrt{x+2}\left(1-\sqrt{x-2}.\sqrt{x+2}\right)=0\)
<=>\(\left\{{}\begin{matrix}\sqrt{x-2=0}\\\sqrt{x+2=0}\\1-\sqrt{x-2}.\sqrt{x+2}=0\end{matrix}\right.\)
<=>\(\left\{{}\begin{matrix}x-2=0\\x+2=0\end{matrix}\right.\)
<=>\(\left\{{}\begin{matrix}x=2\\x=-2\end{matrix}\right.\)
c)\(\sqrt{2x-1}=x-3\)
<=>\(2x-1=\left(x-3\right)^2\)
<=>\(2x-1-x+6x-9=0\)
<=>7x=10
<=>x=\(\frac{10}{7}\)
