Question: How to solve this system of equations symbolically and get a "meaningful" solution


I am trying to solve a system of equations involving several symbols. The answer I am getting involves rootof...
I have tried to fix it, and read several post on MP, but in vain. Please help me to get a solution which does not involve root of solutions. Coz the paper I am follwing has a very elegant solution to these equations which i am failed to obtain via

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