Decay of a particle of mass M into two particles

[Forco]

Homework Statement

A particle of mass M and 4-moment P decays into two particles of masses m₁ and m₂
1) Find the total energy of each particle (lab frame).
2) Show that the kinetic energy T₁ of the first particle in the same reference frame is given by
$$T_1= \Delta M (1 - \frac{m_1}{M} - \frac{\Delta M}{2M}) $$
3) A pion (M= 139.6 MeV) decays into a muon (m=105,7 MeV) and a neutrino (m=0). Find the kinetic energy of the muon and the neutrino (pion rest frame and lab frame).

Homework Equations

$$ E_1+E_2 = Mc^2$$
$$E_{1}^{2} +\frac{p^2}{c^2} = m_{1}^{2} c^4$$
$$E_{2}^{2} +\frac{p^2}{c^2} = m_{2}^{2} c^4$$

The Attempt at a Solution

I was able to do the first one, since it was really simple, I only needed to set

$$E_{1}^{2} - m_{1}^{2} c^4 = E_{2}^{2} - m_{2}^{2} c^4$$
And since $$ E_1+E_2 = Mc^2$$, it was easy to find that
$$E_1 = \frac{M^2+m_{1}^{2}-m_{2}^{2}}{2M}$$
Which is the correct expression for the energy. I'm having some trouble with the other two though. Especially the second one.
Any help is appreciated.

 

[vela]

I was able to do the first one, since it was really simple, I only needed to set

$$E_{1}^{2} - m_{1}^{2} c^4 = E_{2}^{2} - m_{2}^{2} c^4$$
And since $$ E_1+E_2 = Mc^2$$, it was easy to find that
$$E_1 = \frac{M^2+m_{1}^{2}-m_{2}^{2}}{2M}$$
Which is the correct expression for the energy.

Are you sure? I don't see how you can justify equations you started with in the lab frame.