according to your condition in question 3 times heat must be produced in resitor when ac current is passed

heat produced is calculated as  i**2R hence

on equalting both the energy we finally get ......

the following equation :

irms^2 *R*t= 3*idc^2*R*t

irms=2*_/3

irms=3.46

hence on solving we get rms current to be 3.46 A

if you need to find max AC current it would be...

irms * 2

=3.46*2

=6.92