Allied & ICAR Exam Bank • ALLIED_1858 MCQ • 2 Marks

Section 8: General Aptitude

Quantitative Aptitude

Subtopic: Numerical Computation

Question Statement:

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

Options:

  • (A) 4
  • (B) $2\sqrt{3}$
  • (C) $\sqrt{7}$
  • (D) 2

Answer Key:

A

Step-by-Step Solution & Explanation

$7 + 4\sqrt{3} = (2 + \sqrt{3})^2 \implies x = 2 + \sqrt{3}$. $1/x = 2 - \sqrt{3}$. $x + 1/x = 4$.
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