Question

If n = ($\sqrt{7}$ - $\sqrt{3}$)/ ($\sqrt{7}$ +$\sqrt{3}$), then what is the value of N + (1/N)

• A. 2$\sqrt{2}$
• B. 5
• C. 10
• D. 13

Answer 1

The correct option is B 5

Given,

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

now,

$N+\frac{1}{N}$

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

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

$=\frac{10-2\sqrt{21}+10+2\sqrt{21}}{7-3}$

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