This is probably not very exciting, but can't get my head around this for a while. Here's the inequality: $ x_1^3-\epsilon x_1^2 -(2+\epsilon(1-x_1^n))x_1+(1+\epsilon)>0 $ where $\epsilon>0, n \in \mathbb{Z^{+}}$. Please just give me hints, don't solve it for me.
EDIT: $x_1>0$
EDIT2: it seems that the solution to inequality $1-x_1-x_1^2>0$ is the trick. For (see EDIT 1) $0