I am struggling with a practice problem regarding the following reaction:
\begin{equation} \nu_{\mu}+n\rightarrow\mu^{-}+p \end{equation}
The question is "What is the minimum energy of the muon neutrino for the reaction to occur on a neutron initially at rest?". The question is supposed to be solved by assuming that $m_{p}=m_{n}$ without quoting their values. Furthermore, the mass of the muon is provided and the neutrino mass is neglected.
In my attempt to answer the question I have obtained the following relationship from conservation of the energy-momentum four-vector:
\begin{equation} \sqrt{2E_{\nu_{\mu}}m_{n}+m_{n}^{2}}=m_{\mu}+m_{p} \end{equation}
In order, to solve the question I am trying to eliminate $m_{n}$ and $m_{p}$ from this equation. How would one do this?