$\sqrt{x}+$ $\sqrt{2x-1}=2$
$⇔x+2x-1+2\sqrt{x(2x-1)}=4 $
$⇔3x+2\sqrt{2x^2-x}=3$
$⇔2\sqrt{2x^2-x}=3-3x$
$⇔2\sqrt{2x^2-x}=3(1-x)$
$⇔4(2x^2-x)=9(1-x)^2$
$⇔8x^{2}-4x=9(1-2x+x^2)$
$⇔8x^{2}-4x=9-18x+9x^2$
$⇔x^{2}-14x+9=0$
\(⇔\left[ \begin{array}{l}x=7+2\sqrt{10}\\x=7-2\sqrt{10}\end{array} \right.\)