Solving system of 7 equations doesn't finish

Questions
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1

Dear All,

(This is a Mathematics problem. Solving an equation)

I try to solve this system of equations (eq2). To do this, I set each one Equal zero, so I will have a system of 7 equations. I also considering 7 unknowns and I am trying to solve it with the Solve command, but no matter how much I wait, Mathematica does not give me an answer. Do you know what the problem is?

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2

I thought I saw what the problem was. Now I see that I was mistaken. I’m sorry.

3

It is a polynomial system of high degree in 7 variables with 4 parameters. We can expect it to be quite difficult. Try giving numerical values to the parameters to get a feeling for what may happen:

coefficients /. {k -> 0, \[Mu] -> 0, \[Eta] -> 0, \[Beta] -> 
    1} // Simplify
Solve[% == 0]
4

If I only eliminate only 2 parameters I have answer with 100 pages of solution.

Analytical solving seems impossible.

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Regards M.I.

5

I’m so grateful.

I wanted the answer I highlighted in red, but how do I guess the conditions for the rest of the questions?

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