Question

If x = $\sqrt{7 + 4\sqrt{3}}$, then x + $\frac{1}{x}$is equal to-

• A. 4
• B. 6
• C. 3
• D. 2

Answer 1

Answer: (A)

4

Answer 2

x = $\sqrt{7 + 4\sqrt{3}}$= $\sqrt{4 + 3 + 2.2.\sqrt{3}}$

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

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

x + $\frac{1}{x}$ = (2 + $\sqrt{3}$) + (2 – $\sqrt{3}$) = 4