We apply conservation of (relativistic) energy and conservation of (relativistic) momentum. Let denote the energy of the photon that was destroyed. The initial momentum is and the initial energy is
We are told that the positron and the two electrons move off with the same speed at the end. So, they must each have a momentum equal to . Therefore, the total energy at the end is
Equating the initial and final energies and then squaring both sides of the equation, we find that
Therefore, answer (D) is correct.