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

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

I think the title should be (a + √ 3b) &# 178; = 3 + A & # 178; - 4 √ 3
∵(a+√3b)²=3+a²-4√3
a²+2√3ab+3b²=3+a²-4√3
∴（2ab+4)√3+3b²-3=0,
∵ a, B are rational numbers,
∴2ab+4=0,3b²-3=0,
A = 2, B = - 1 or a = - 2, B = 1,
In ∵ √ a, a ≥ 0,
∴a=2,b=-1,
∴√a+b=√2-1．
If you insist on your question, the answer is as follows
∵(a+√3b)²=3+a²-a√3
a²+2√3ab+3b²=3+a²-a√3
∴（2ab+a)√3+3b²-3=0,
∵ a, B are rational numbers,
∴2ab+a=0,3b²-3=0,
A = 0, B = - 1 or a = 0, B = 1,
∴√a+b=±1．