x = 2 + 3^(1/2) therefore : x^2 = 4 + 3 + 4(3)^(1/2)= 7 + 4(3)^(1/2)
and 1/x^2 = 1/ [7+4(3)^(1/2)] =[7-4(3)^(1/2)]/{[7+4(3)^(1/2)][7-4(3)^(1/2)]} = [7-4(3)^(1/2)]
since : (x^2 + 1/x^2)^2 = x^4 + 1/x^4 + 2
therefore : x^4 + 1/x^4 = (x^2 + 1/x^2)^2 - 2 = [ 7+ 4(3)^(1/2) + 7 - 4(3)^(1/2)]^2 - 2 = 14^2 -2 = 196 -2 = 194