That is what I did, not getting anywhere. x=ω2 and A, B, C= ω2A B or Cx2 - x(A+B+C) +[AC+AB+BC]
doing the quadratic formula
x = (A+B+C)/2 ± ½√(A2+B2+C2-3AB-3BC-3AC)
I don't think that is moving in the right directing judging by the answer in the back (ω'2 = (kA+kB+kC)/m and ω''2 = kC/m)