i have a system of equations in which there are two parameters F, G. I choose F,G positive. the code is:
G > 0
F > 0
Reduce[{(1/Sqrt[V (Z *H*P - V*MU)]) == (F*G)^(-1/2),
Sqrt[(Z *H*P - V*MU)/V] Z^-1 == (F/G)^(1/2),
Sqrt[(Z *H*P - V*MU)/V] H^-1 == (G/F)^(1/2),
Sqrt[(Z *H*P - V*MU)/V] P^-1 == (F*G)^(
1/2), ((Z *H*P - V*MU)^(3/2)/(V^(3/2)*Z *H*P) ) == (F*G)^(1/2),
MU == 0}, {V, Z , H, P, MU}, Reals]
But i obtain this:
((G < 0 && F < 0 && V == 1 && Z == -G && H == (F G)/Z &&
P == (H Z)/(F G)) || (G > 0 && F > 0 && V == 1 && Z == G &&
H == (F G)/Z && P == (H Z)/(F G))) && MU == 0
Why? I choose F,G positive and why it considers all the possibility? Another thing is it finds the value , for example, of Z but it doesn't substitute it into the result of H and P.
Thank you