If 2+root3/2-root/3 + 2-root3/2+root3 = a+b root3 find the values of a and b

To solve for 2 variables, you need 2 equations. The best you could do with only one equation would be to find 'a' in terms of 'b'. Just looking it over and without putting pen to paper, it looks to me like one possible solution is [ a = 4, b = 0 ].