If N = 7 - 3 7 + 3 , then what is the value of N + 1/N?

Answer: Option B

$$\begin{array}{rl}& N=\frac{\sqrt{7}-\sqrt{3}}{\sqrt{7}+\sqrt{3}}\\ & =\frac{\sqrt{7}-\sqrt{3}}{\sqrt{7}+\sqrt{3}}\times \frac{\sqrt{7}-\sqrt{3}}{\sqrt{7}-\sqrt{3}}\\ & =\frac{7+3-2\sqrt{21}}{4}\\ & =\frac{10-2\sqrt{21}}{4}\\ & =\frac{5}{2}-\frac{\sqrt{21}}{2}\\ & \text{Similarly }\frac{1}{N}=\frac{5}{2}+\frac{\sqrt{21}}{2}\\ & \therefore N+\frac{1}{N}\\ & =\frac{5}{2}-\frac{\sqrt{21}}{2}+\frac{5}{2}+\frac{\sqrt{21}}{2}\\ & =\frac{5}{2}+\frac{5}{2}\\ & =5\end{array}$$