Answer
$x=1$
Work Step by Step
$\sqrt {5x-1} -\sqrt x +2=3$
$\sqrt {5x-1} -\sqrt x +2+\sqrt x-2=3+\sqrt x-2$
$\sqrt {5x-1} = 1+\sqrt x$
$(\sqrt {5x-1})^2 = (1+\sqrt x)^2$
$5x-1 = 1*1+1*\sqrt x+\sqrt x*1+\sqrt x*\sqrt x$
$5x-1 = 1+2*\sqrt x+x$
$5x-1+1 = 1+2*\sqrt x+x+1$
$5x= 2+2*\sqrt x+x$
$5x-x= 2+2*\sqrt x+x-x$
$4x= 2+2*\sqrt x$
$4x-2= 2+2*\sqrt x-2$
$4x-2= 2\sqrt x$
$(4x-2)/2= 2\sqrt x/2$
$2x-1= \sqrt x$
$(2x-1)^2= (\sqrt x)^2$
$2x*2x+2x*(-1)+(-1)*2x+(-1)(-1)=x$
$4x^2-2x-2x+1=x$
$4x^2-4x+1=x$
$4x^2-5x+1=0$
$4x^2-4x-x+1=0$
$(4x^2-4x)-(x-1)=0$
$4x(x-1)-1(x-1)=0$
$(4x-1)(x-1)=0$
$4x-1=0$
$4x=1$
$4x/4=1/4$
$x=1/4$
$x-1=0$
$x=1$
$\sqrt {5*1/4-1} -\sqrt {1/4} +2=3$
$\sqrt {5/4-1} -1/2 +2=3$
$\sqrt {1/4} +3/2=3$
$\sqrt {1/4} +3/2=3$
$1/2 + 3/2=3$
$4/2=3$
$2=3$ (false)
$\sqrt {5x-1} -\sqrt x +2=3$
$\sqrt {5*1-1} -\sqrt 1 +2=3$
$\sqrt {5-1} -1 +2=3$
$\sqrt {4} +1=3$
$2+1=3$ (true)
