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How to solve this two simultaneous equations?

these two equations got from this free energy equation 

 f=1/2 (T - 1) P^2 + 1/4 P^4 +1/2 α^2 (β) Tmp (T - Tmp) M^2 + 1/4 α^2 (β)Tmp^2 (M^4) + ρ (P^2) (M^2)

then i first derivative the equation

fp=D[f,P] fm=D[f,M] which then got the a and b below.

I don't want imaginary and negative answer. In terms of $M$ and $P$

fp=P^3 + P (-1 + T) + 2 M^2 P ρ  

fm=M (T - Tmp) Tmp α^2 β + M^3 Tmp^2 α^2 β + 2 M P^2 ρ

I already use Solve[{fp==0,fm==0},{M,P} Reals] also already use Solve[{fp==0&&fm==0},{M,P} Reals] and Reduce[{fp==0,fm==0,M>0,P>0},{M,P}] and got a series of solution. already put it in the code and the graph is kinda'weird'

Tmp, alpha, beta, rho, and T you don't have to mind their value. the value of $P$ and $M$ i must use to plot the graph of "M/P againt T" the thing is i did not get the right graph because these $P$ and $M$ value is incorrect which is not simultaneously solve correctly.

**how to copy whole code that i did into this question? thank you in advance

Nabil
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  • Greetings! To make the most of Mma.SE please take the [tour] now. Help us to help you, write an excellent question. Edit if improvable, show due diligence, give brief context, include minimum working examples of code and data in formatted form. As you receive give back, vote and answer questions, keep the site useful, be kind, correct mistakes and share what you have learned. – rhermans Jan 22 '16 at 10:17
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    In your Solve command, you have b==o, but I think you wanted b==0 – Jason B. Jan 22 '16 at 10:22
  • Your question may be put on-hold as it seems to be off-topic, i.e it arises from a simple mistake (syntax error, incorrect capitalization, spelling mistake) and is unlikely to help any future visitors, or else it is easily found in the documentation. Don't be discouraged by that cleaning-up policy. Your future good questions are welcome. Learn about common pitfalls here. – rhermans Jan 22 '16 at 10:54
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    I'm voting to close this question as off-topic because even with typo fixed, it becomes a misunderstanding of the mathematics rather than Mathematica per se. – Daniel Lichtblau Jan 22 '16 at 16:13
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    As long as the various parameters are unspecified there is no way to enforce positivity in a symbolic solution. – Daniel Lichtblau Jan 22 '16 at 16:14
  • You really need to make a better effort on explaining yourself. It's very hard to offer a solution to:"the graph is kinda'weird'". Please help us to help you by writing a good question. Follow the links provided in the previous comments as a first step, they do contain useful information. – rhermans Jan 23 '16 at 10:36

1 Answers1

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Try constraining the domain to Reals

Solve[{a == 0, b == 0}, {M, P},Reals]

You may want to look also into Reduce

Reduce[{a == 0, b == 0, M > 0, P > 0}, {M, P}, Reals]
rhermans
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  • hye @rhermans, i updated the question. how to show you my work? – Nabil Jan 23 '16 at 10:25
  • Please start by reading this help on how to ask a good question: http://mathematica.stackexchange.com/help/how-to-ask Also read this other question on how to share code http://meta.mathematica.stackexchange.com/questions/2/how-should-i-include-code-samples-in-posts – rhermans Jan 23 '16 at 10:31