What is the best way to solve inequalities with multiple variables of possibly higher degrees as well? Any method, by hand or software will do.
Want solution similar to this:
$$f(a,b) \geq 0$$ Solution:
$$a \in (-k,k)$$ $$b \in (-a, a)$$
As in, the variables can be dependent on each other (as they will in several situations.)
Edit:
The specific questions I'm trying to solve are:
\begin{align*} &1. -\frac{1}{18}((a^2-1)^2 - a^2)p + \frac{1}{18} \geq 0 \text{ and } -\frac{1}{108}((a^2-1)^2 - a^2)p + \frac{1}{108} \lt 0 \\ &2. -\frac{1}{18}((a^2-1)^2 - a^2)p + \frac{1}{18} \geq 0 \text{ and } -\frac{1}{324}a^8p^2 + \frac{1}{54}a^6p^2 - \frac{11}{324}a^4p^2 + \frac{1}{54}a^2p^2 + \frac{1}{324}p^2 + \frac{1}{432} \lt 0\\ \end{align*} (Two separate questions)