= Solution
Denote the parent <rest mass> by $M$, the daughter <rest masses> by $m_i$, and their total energies in any <inertial frame> by $E_{\rm before}$ and $E_{\rm after}$. For an isolated disintegration with all products included, <energy> conservation gives $E_{\rm after}=E_{\rm before}$. The corresponding <kinetic energies> are $K_{\rm before}=E_{\rm before}-Mc^2$ and $K_{\rm after}=E_{\rm after}-\sum_i m_ic^2$. Consequently
$$
\boxed{\Delta K=K_{\rm after}-K_{\rm before}=\left(M-\sum_i m_i\right)c^2.}
$$
Every <mass> on the right is a <rest mass>, hence invariant under a <Lorentz transformation>. This proves the <kinetic energy> released by relativistic decay is frame independent even though either total <kinetic energy> separately is not. In the parent <rest frame> the initial <kinetic energy> vanishes and the final <kinetic energy> equals the <energy> associated with this <mass defect>. External <energy> input or omission of radiation would invalidate the energy-cancellation step; if <photons> are products, include their energies with zero rest-mass subtraction.
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