If 4 + 3 3 7 + 4 3 = A + B , then B - A is = ?

Answer: Option C

$$\begin{array}{rl}& \frac{4+3\sqrt{3}}{\sqrt{7+4\sqrt{3}}}\text{ = }A+\sqrt{B}\\ & \Rightarrow \sqrt{7+4\sqrt{3}}\\ & \Rightarrow \sqrt{2^2+{\left(\sqrt{3}\right)}^2+2\times 2\sqrt{3}}\\ & \Rightarrow \sqrt{{\left(2+\sqrt{3}\right)}^2}\\ & \Rightarrow \left(2+\sqrt{3}\right)\\ & \Rightarrow \frac{4+3\sqrt{3}}{2+\sqrt{3}}\text{ = }A+\sqrt{B}\\ & \Rightarrow \frac{4+3\sqrt{3}}{2+\sqrt{3}}\times \frac{2-\sqrt{3}}{2-\sqrt{3}}=A+\sqrt{B}\\ & \Rightarrow \frac{\left(4+3\sqrt{3}\right)\left(2-\sqrt{3}\right)}{4-3}=A+\sqrt{B}\\ & \Rightarrow 8-4\sqrt{3}+6\sqrt{3}-9=A+\sqrt{B}\\ & \Rightarrow 2\sqrt{3}-1=A+\sqrt{B}\\ & \therefore A=-1\&\sqrt{B}=2\sqrt{3}\\ & \because B=2\sqrt{3}\times 2\sqrt{3}=12\\ & \text{So},B-A=12-\left(-1\right)=13\end{array}$$