two balls of similar size masses m and 2m are moving at speeds u and 2u along a frictionless plane, they collide head on and are reflected, assuming that the coefficient of restitution of this collision is 1, what the speeds are afterwards in u

ball A has mass m and velocity u. ball B has mass 2 m and velocity 2uby conservation of momentum:mu - 4mu = mv + 2mx (1)where v is the velocity of ball A and x is the velocity of ball B after collision.by conservation of energy:1/2mu^2 + 4mu^2 = 1/2mv^2 + mx^2 (2)equation (1) can be rearranged to become:v= -3u + 2x (3)substituting (3) into (2) 1/2mu^2 +4mu^2 = 1/2m(-3u + 2x)^2 +mx^2 (4)simplifying and grouping terms in (4) and moving to one side to make a quadratic gives:0=5x^2 - 12ux, this means that x must be either 0 or -2usubstituting these results into our term for momentum (1)v is either -3u or u, evidently the answer must be that x is 0 and v is -3u