Answer
$\{-3, 1\}$
Work Step by Step
Step 1. Given the equation $\sqrt[4] {x^2+2x}=\sqrt[4] {3}$
Step 2. Raise to the 4th power on both sides to get: $x^2+2x=3$ or $x^2+2x-3=0$ which gives $x=-3,1$
Step 3. Check answer in the original equation: both $\{-3, 1\}$ fit.
