Answer
$(-\infty,-1)\cup(1,\infty)$.
Work Step by Step
Step 1. For $x^4-x^2\gt0 \Longrightarrow x^2(x+1)(x-1)\gt0$, identify boundary points as $x=-1,0,1$.
Step 2. Form intervals $(-\infty,-1),(-1,0),(0,1),(1,\infty)$.
Step 3. Choose test values for each interval $x=-2,-0.5,0.5,2 $.
Step 4. Test the inequality to get results: $True,\ False,\ False,\ True$
Step 5. We have the solution $(-\infty,-1)\cup(1,\infty)$.
