Two particle decay

A particle with momentum P decays into two particles travelling colinearly with the parent particle.  What is the momenta of the daughter particles.  If the parent is a pion (mass .139 GeV/c^2) with momentum of 250 GeV/c and the daughters are a muon (mass = .105 GeV/c^2) and a neutrino (mass = 0), what are the two possible momenta of the neutrino?

Solution:

Conservation of energy:

eq1  =  E0  ==  E1 +  E2

Conservation of momentum:

eq2  =  p0  ==  p1 + p2

Constituent Equations:

eq3  =  E0 == Sqrt[p0^2  +  m0^2]
eq4  =  E1  ==  Sqrt[p1^2 + m1^2]
eq5  =  E2  ==  Sqrt[p2^2 + m2^2]

Solve equations:

solution  =  
      Simplify[Solve[{eq1, eq2, eq3, eq4, eq5}, {E0, E1, E2, p1, 
            p2}]]

conditions = {p0 -> 250. , m0 ->  .139, m1 ->  .105, 
        m2 -> 0. }

{p1, p2} /. (solution /. conditions)