= Solution
In the <pion> <rest frame>, <momentum conservation> makes the <muon> and <neutrino> momenta opposite, with common magnitude $p$. For a massless <neutrino>, $E_\nu=pc$; <energy conservation> and the <relativistic energy-momentum relation> give
$$
E_\mu+pc=m_\pi c^2,\qquad E_\mu^2-p^2c^2=m_\mu^2c^4.
$$
Substitute $pc=m_\pi c^2-E_\mu$ into the second equation. The $E_\mu^2$ terms cancel, leaving
$$
\boxed{E_\mu=\frac{m_\pi^2+m_\mu^2}{2m_\pi}c^2.}
$$
For completeness, the complementary <relativistic two-body decay> energy is $E_\nu=(m_\pi^2-m_\mu^2)c^2/(2m_\pi)$. The result is a total <energy>, including the <muon> <rest energy>, rather than its <kinetic energy>.
Back to article page