Chapter 1, Equations and Graphs - Chapter 1 Review - Exercises - Page 170: 61

$x=1$

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