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Question: How do I Characterize these equations in terms of solutions?

Question:How do I Characterize these equations in terms of solutions?

Thomas Dean 322 Maple
solve extrema plotting
December 22 2022
1

How do I characterize this equation set? I think it has 6 solutions, equal in pairs, or 3 distinct solutions.

restart;

eq1 := x = (((72*5^(3/2)+270)*a^2-1344*5^(3/2)*a)*w+(9*5^(5/2)-1485)*a^2-2016*5^(3/2)*a-12544*5^(5/2))/(((288*sqrt(5)+216)*a^2-5376*sqrt(5)*a)*w+(36*5^(3/2)-1188)*a^2-8064*sqrt(5)*a+6272*5^(3/2)):

eq2:= a^3 = -(128*5^(5/2)*w)/9+(1600*w)/3+(544*5^(3/2))/9+15200/27:

eq3:=1+w+w*w = 0:##   or w = (sqrt(3)*%i)/2-1/2;

for s1 in [solve(eq2,a)] do
    for s2 in [solve(eq3,w)] do
        subs(a=s1, eq1):
        subs(w=s2,%):
        lprint("sol",simplify(%));
    end do;
end do;
 
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