Question

If $x=2+\sqrt{3}$, then $(x+\frac{1}{x})$ equal to :

• A. $-2\sqrt{3}$
• B. $2$
• C. $4$
• D. $4-2\sqrt{3}$

Answer 1

Answer: (C)

$4$

$x+\frac{1}{x}=2+\sqrt{3}+\frac{1}{2+\sqrt{3}}=2+\sqrt{3}+\frac{2-\sqrt{3}}{(2+\sqrt{3})\times (2-\sqrt{3})}=2+\sqrt{3}+\frac{2-\sqrt{3}}{2^2-{\sqrt{3}}^2}=2+\sqrt{3}+\frac{2-\sqrt{3}}{4-3}=2+\sqrt{3}+2-\sqrt{3}=4$