# solve this

Question:

If $x=2+\sqrt{3}$ then $\left(x+\frac{1}{x}\right)$ equals

(a) $-2 \sqrt{3}$

(b) 2

(c) 4

(d) $4-2 \sqrt{3}$

Solution:

$x=2+\sqrt{3}$

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

$x+\frac{1}{x}=2+\sqrt{3}+2-\sqrt{3}=4$

Hence, the correct answer is option (c).

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