a^2+2ab+b^2=12 => (a+b)(a+b)=12 (1)
a^2-b^2=4√3 => (a+b)(a-b)=4√3 (2)
(1)÷(2) (a+b)/(a-b)=12/4√3=3/√3=√3
(a-b+2b)/(a-b)=√3
1+2b/(a-b)=√3
2b/(a-b)=√3-1
b/(a-b)=(√3-1)/2
即(a-b)/b=2/(√3-1)=√3+1