Chapter 1, Equations and Graphs - Section 1.6 - Solving Other Types of Equations - 1.6 Exercises - Page 139: 63

$x=5$

$x^{3/2}-10x^{1/2}+25x^{-1/2}=0$ $x^{-1/2}(x^{2}-10x+25)=0$ $x^{-1/2}(x-5)^{2}=0$ $x^{-1/2}=0$ or $(x-5)^{2}=0$ $\frac{1}{\sqrt{x}}=0$ or $x=\sqrt{0}+5=5$ The left equation has no solution, so the only solution is $x=5$