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Question: Difficulty Verifying Maple's Solution to a Nonlinear System

Question:Difficulty Verifying Maple's Solution to a Nonlinear System

emendes 515 Maple 2025
solve radical simplify assumptions simplification
May 25 2025
2

Hello,

I am working with the following overdetermined system of nonlinear equations in Maple and attempting to solve it for the unknowns xi[3] and xi[8].

[sqrt(beta*rho*xi[8]^2 - beta*xi[8]^2)/xi[8] = sqrt(beta*rho - beta), (-rho + 1 + sqrt(beta*rho*xi[8]^2 - beta*xi[8]^2))/(xi[3]*xi[8] - 1) = sqrt(beta*rho - beta), -(-rho*xi[3]*xi[8] + sqrt(beta*rho*xi[8]^2 - beta*xi[8]^2) + xi[3]*xi[8])/(xi[8]*(xi[3]*xi[8] - 1)) = rho - 1]

Maple returns the following solution:

{xi[3] = (-rho + sqrt(beta*(rho - 1)) + 1)/sqrt(beta*(rho - 1)), xi[8] = -(-rho + sqrt(beta*(rho - 1)) + 1)/(rho - 1)}

However, when I substitute the solution back into the original equations, the left-hand side should equal the right-hand side. Yet, using simplify(subs(solution, equation)) does not reduce the expression sufficiently to verify the equality.

Am I missing something in the simplification process?

Many thanks,

Ed
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