#### Answer

$x=1$

#### Work Step by Step

$x^{-1/2}-2x^{1/2}+x^{3/2}=0$
$x^{-1/2}(1-2x+x^{2})=0$
$x^{-1/2}(1-x)^{2}=0$
$\frac{1}{\sqrt{x}}(1-x)^2=0$
$\frac{1}{\sqrt{x}}=0$ or $(1-x)^2=0$
The left equation has no solution (since that would require division by 0). The right equation gives:
$(1-x)^{2}=0$
$1-x=0$
$x=1$