Logan D. answered 01/17/15
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Calculus
The conservation of energy tells us that energy conserved. Thus, the energy of the recoil is equal and opposite the energy of the bullet. Since the gun has a larger mass, then it must compensate by having a smaller velocity; and since the bullet has a smaller mass, then it must compensate by having a larger velocity.
Since velocity is squared with KE (0.5mv2), then the bullet will have a higher KE than the gun.