Chapter 1 - Equations and Inequalities - 1.8 Absolute Value Equations and Inequalities - 1.8 Exercises - Page 169: 91

$\{\pm1 \}$

Step 1. Rewrite the equation as $|x^2+1|=|2x|$. Remove the absolute value sign to get $x^2+1=2x$ and $x^2+1=-2x$ Step 2. For $x^2+1=2x$, we have $x^2-2x+1=0$ which gives $x=1$ Step 3. For $x^2+1=-2x$, we have $x^2+2x+1=0$ which gives $x=-1$ Step 4. Combine the above results, we have the solution set as $\{\pm1 \}$