elastic collision

 

I have a doubt, in an inelastic collision, the kinetic energy is not conserved but momentum is conserved, now assuming masses of the bodies remain the same , i dont understand that how it is possible that although momentum is conserved but not the kinetic energy.

If masses are same

m(u1+u2) = -m(v1+v2) momentum coservation

Now for v1 and v2 can have different values, may be some with KE increasing,KE decreasing and KE equal. Out of this if it is inelastic definitly the KE will be less due to some loss.