I was studying inequations when I encountered this problem here.
How can I find a region of values for m where this inequation is true?
$$-3<\frac{x^2+mx-2}{x^2-x+1}>2$$
Thanks
2026-04-22 21:40:44.1776894044
Inequality challenge
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you have to solve two polynomial equations.
It's obvious that $x^{2}-x+1>0$. Then the inequality becomes:
\begin{equation} -3x^{2}+3x-3<x^{2}+mx-2<2x^{2}-2x+1 \end{equation}
which is easy to solve, see for instance http://en.wikipedia.org/wiki/Quadratic_function