This is a similar question with this one. But with a bit of twist.
I have two inequalities:
$$y_{1min} \leq y_{1}(x_1,x_2) \leq y_{1max}$$ $$y_{2min} \leq y_{2}(x_1,x_2) \leq y_{2max}$$
where
$$y_i(x_1,x_2)=\Biggl[\frac{(x_{1}^2x_{2}+b_{i}x_{1}x_{2}+c_{i})^{f_i}}{(x_{1}(2+x_{2})+e_{i})^{g_i}}\Biggr]$$
where $f_1=g_1=1, f_2=5, g_2=2.$
$b_{i},c_{i},e_{i},x_1,x_2\in\mathbb{R}$
Question: How to find the range of $x_{1},x_{2}$ that satisfy the above inequalities?
The range of $x_{1},x_{2}$ is defined as all the $x_1,x_2$ pairs that satisfy the above inequalities.
Edit: Maybe I'll relax the question a bit: let's assume that $b_{1}=b_{2}, c_{1}=c_{2}, e_{1}=e_{2}$.