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(3-2√3)(4+a√3) = b-23√3
12-8√3+3a√3-6a = b-23√3
12-6a+(3a-8)√3 = b-23√3
By comparison
3a-8 = -23
3a = -15
a = -5
12-6a = b
12-6(-5) = b
b = 42
12-8√3+3a√3-6a = b-23√3
12-6a+(3a-8)√3 = b-23√3
By comparison
3a-8 = -23
3a = -15
a = -5
12-6a = b
12-6(-5) = b
b = 42