Chapter 1 - Equations and Inequalities - 1.6 Other Types of Equations and Applications - 1.6 Exercises - Page 148: 104

$\{\pm\frac{5}{2},\pm5\}$

Step 1. Let $u=(x)^{-2}$, we have $625u^2-125u+4=0$ Step 2. Factor and solve: $(25u-4)(25u-1)=0$ thus $u=\frac{1}{25}, \frac{4}{25}$ Step 3. For $u=\frac{1}{25}$, we have $(x)^{-2}=\frac{1}{25}$ thus $x=\pm5$ Step 4. For $u=\frac{4}{25}$, we have $(x)^{-2}=\frac{4}{25}$ thus $x=\pm\frac{5}{2}$ Step 5. Solution set $\{\pm\frac{5}{2},\pm5\}$