Question

If $\frac{\sqrt{3}-1}{\sqrt{3}+1}=a+b\sqrt{3}$, then the value of 𝒂 and 𝒃 is

Answer 1

Option(a)
$\frac{\sqrt{3}-1}{\sqrt{3}+1}\times \frac{\sqrt{3}-1}{\sqrt{3}-1},\frac{{(\sqrt{3}-1)}^2}{{\left(\sqrt{3}\right)}^2-{\left(1\right)}^2},\frac{{(\sqrt{3}-1)}^2}{3-1},\frac{{(\sqrt{3}-1)}^2}{2},\frac{{[{\left(\sqrt{3}\right)}^2+(1)}^2-2\times 1\times \sqrt{3}]}{2},\frac{[4-2\sqrt{3}]}{2},2-\sqrt{3},$

Upon comparing with RHS of given question,
$a=2,b=-1$