3 phase AC circuit problem
Two things:


You calculated the average transferred power. You have calculated it right. You use RMS value phasors, the book uses peak values. That explains the factor 2.
The book wanted the instantneous power to the load. There's a proof that in every moment the total power is the same. Your calculation gives no info about how power transfer varies during one AC voltage cycle. Your calculation is NOT a proof for the fact that the total power transfer is constant (=the same in every moment).