Let's say I have a function parameterized by a number of variables. As a simple example $$F(x,y) = ax^2 +by^2-cxy+1$$ I want to find some set of values (doesn't really matter what they are) for the parameters so that the relation $$ F(x,y)>0$$ holds for all points of its domain. So I would want values returned like (1,1,1). I don't need all possible values, just one example where the relation holds.
Is there a function in Mathematica that could do this? The real function I need to operate on is way more complicated and has a few more parameters, but can this be done simply?
I know of
SolveAlways, but it doesn't like it when I apply relations instead of equalities.
I appreciate any help!