Verified answer

[ (√3 - 1)(√3 - 1) ] / [ (√3 + 1)(√3 - 1) ]

= [ 3 - 2√3 + 1 ] / [ 3 - 1 ]

= (4 - 2√3) / 2

= 2 - √3

Comparing this with the expression a + b√3, we can equate the coefficients of √3:

a = 2

b = -1