Given that a and B are rational numbers and (a + √ 3b) ^ 2 = 7-4 √ 3, find the value of a and B

Complete square, (a + √ 3b) ^ 2
=a^2+(√3b)^2+2√3ab
=a^2+3b^2+2√3ab=7-4√3
From the question a ^ 2 + 3B ^ 2 = 7 (*), 2 √ 3AB = - 4 √ 3
That is, ab = - 2, a = B of minus 2, if (*), a = 2 or a = - 2,
When a = 2, B = - 1, when a = - 2, B = - 1

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