8:
a: ĐKXĐ: \(x\in R\)
\(\sqrt{\left(x-3\right)^2}=3-x\)
=>|x-3|=3-x
=>x-3<=0
=>x<=3
b: ĐKXĐ: \(x\in R\)
\(\sqrt{4x^2-20x+25}+2x=5\)
=>\(\left|2x-5\right|=5-2x\)
=>2x-5<=0
=>x<=5/2
c: ĐKXĐ: \(x\in R\)
\(\sqrt{36x^2-12x+1}=5\)
=>|6x-1|=5
=>6x-1=5 hoặc 6x-1=-5
=>6x=6 hoặc 6x=-4
=>x=-2/3 hoặc x=1
9:
a: ĐKXĐ: \(\left\{{}\begin{matrix}2x+5>=0\\1-x>=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x>=-\dfrac{5}{2}\\x< =1\end{matrix}\right.\)
\(\sqrt{2x+5}=\sqrt{1-x}\)
=>2x+5=1-x
=>3x=-4
=>x=-4/3(nhận)
b: ĐKXĐ: \(\left\{{}\begin{matrix}x^2-x>=0\\3-x>=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x< =3\\\left[{}\begin{matrix}x>=1\\x< =0\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}1< =x< =3\\x< =0\end{matrix}\right.\)
\(\sqrt{x^2-x}=\sqrt{3-x}\)
=>x2-x=3-x
=>x2=3
=>\(x=\sqrt{3}\left(nhận\right);x=-\sqrt{3}\left(nhận\right)\)
c: ĐKXĐ: \(\left\{{}\begin{matrix}2x^2-3>=0\\4x-3>=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x^2>=\dfrac{3}{2}\\x>=\dfrac{3}{4}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\left[{}\begin{matrix}x>=\sqrt{\dfrac{3}{2}}\\x< =-\dfrac{\sqrt{3}}{2}\end{matrix}\right.\\x>=\dfrac{3}{4}\end{matrix}\right.\Leftrightarrow x>=\dfrac{3}{4}\)
\(\sqrt{2x^2-3}=\sqrt{4x-3}\)
=>2x^2-3=4x-3
=>2x^2-4x=0
=>2x(x-2)=0
=>x=2(nhận) hoặc x=0(loại)