b: ĐKXĐ: x>=1/5
\(\sqrt{5x-1}-\sqrt{x}=4x-1\)
=>\(\dfrac{5x-1-x}{\sqrt{5x-1}+\sqrt{x}}=4x-1\)
=>\(\sqrt{5x-1}+\sqrt{x}=1\)
=>\(\left(\sqrt{5x-1}+\sqrt{x}\right)^2=1\)
=>\(5x-1+x+2\sqrt{x\left(5x-1\right)}=1\)
=>\(2\sqrt{5x^2-x}=1+1-6x=2-6x\)
=>\(\sqrt{5x^2-x}=1-3x\)
=>\(\left\{{}\begin{matrix}1-3x>=0\\\left(1-3x\right)^2=5x^2-x\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x< =\dfrac{1}{3}\\9x^2-6x+1-5x^2+x=0\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x< =\dfrac{1}{3}\\4x^2-5x+1=0\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x< =\dfrac{1}{3}\\\left(x-1\right)\left(4x-1\right)=0\end{matrix}\right.\Leftrightarrow x=\dfrac{1}{4}\left(nhận\right)\)
