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Question: How to interpret RootOf Expression?

Question:How to interpret RootOf Expression?

Nawazish13fpm 20 Maple
solve explicit rootof
September 16 2022
0

I've attached a maple file (.mw). After solving the first order condition of SW expression, I tried to obtain an optimal point for en. To do that I used solve API, and obtained a solution in rootof. I want to comment on the relationship of en with other parameters like A, theta, zeta, etc. Therefore, I want to understand the interpretation of rootof and how analytically I can simplify it further if possible.

restart

SW := (1/6)*a*(8*sqrt(epsilon[n]*theta[n]*a)*Zeta[n]+3*a*tau-3*a)+(1/3)*e[n]*(-beta[n]*e[n]^2+3*delta[n]*A+4*sqrt(e[n]*theta[n]*A))

(1/6)*a*(8*(varepsilon[n]*theta[n]*a)^(1/2)*Zeta[n]+3*a*tau-3*a)+(1/3)*e[n]*(-beta[n]*e[n]^2+3*delta[n]*A+4*(e[n]*theta[n]*A)^(1/2))

 (1)

``

NULL

Opt_effort_FOC := diff(SW, e[n])

-(1/3)*beta[n]*e[n]^2+delta[n]*A+(4/3)*(e[n]*theta[n]*A)^(1/2)+(1/3)*e[n]*(-2*beta[n]*e[n]+2*theta[n]*A/(e[n]*theta[n]*A)^(1/2))

 (2)

``

NULL

solve(Opt_effort_FOC = 0, e[n])

RootOf(-A^3*delta[n]*theta[n]^2-2*A^2*_Z*theta[n]^2+_Z^4*beta[n])^2/(theta[n]*A)

 (3)

NULL

``

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