Question

已知a-b=2根号3-1,ab=根号3则(a+b)(a-b)等于

Answer 1

a-b=2√3-1

两边平方

(a-b)²=12-4√3+1

a²-2ab+b²=13-4√3

a²+b²=13-4√3+2ab=13-2√3

(a+b)²

=a²+2ab+b

=13

a+b=±√13

所以原式=±√13(2√3-1)

=2√39-√13或-2√39+√13