MATLAB: Solve a large composite set of equations numerically

Question

I have the following set of equations:

1:

where are known scalar constants, and

2:

3:

where Vis known scalar constant and k is a scalar which I want to find.

4:

5:

I've been informed to find the value of k from the last following two inequalities:

with

and are known constants.

Just to make things little more easier, let

The ultimate problem here is that do not have explicit symbolic equations because I have to compute them numerically since their direct symbolic equations are too complicated and Matlab symbolic engine produces too big output.

So the question is: how to numerically solve inequalities (5:) for the variable k ?

Answer 1

I have finally solved this set symbolically, but this is offtopic, so close it now.