If N =7−37+3 , then what is the value of N + 1N?

B. 5 — N+1N=7−37+3+7+37−3=7−32+7+3272−32=7+3−221+7+3+2214=204=5

Number system — Question 2

SSC CGL · Quantitative Aptitude

If N = $\frac{\sqrt{7} - \sqrt{3}}{\sqrt{7} + \sqrt{3}}$ , then what is the value of N + $\frac{1}{N}$ ?

Correct answer: B

$N + \frac{1}{N} = \frac{\sqrt{7} - \sqrt{3}}{\sqrt{7} + \sqrt{3}} + \frac{\sqrt{7} + \sqrt{3}}{\sqrt{7} - \sqrt{3}}$

$= \frac{{(\sqrt{7} - \sqrt{3})}^{2} + {(\sqrt{7} + \sqrt{3})}^{2}}{{(\sqrt{7})}^{2} - {(\sqrt{3})}^{2}}$

$= \frac{7 + 3 - 2 \sqrt{21} + 7 + 3 + 2 \sqrt{21}}{4}$

$= \frac{20}{4} = 5$