Allied & ICAR Exam Bank • ALLIED_2362 MCQ • 2 Marks

Section 8: General Aptitude

Quantitative Aptitude

Subtopic: Numerical Computation

Question Statement:

If $x = \sqrt[3]{2 + \sqrt{3}} + \sqrt[3]{2 - \sqrt{3}}$, then $x^3 - 3x$ equals:

Options:

  • (A) 4
  • (B) 2
  • (C) 0
  • (D) 1

Answer Key:

A

Step-by-Step Solution & Explanation

Let $a = \sqrt[3]{2+\sqrt{3}}, b = \sqrt[3]{2-\sqrt{3}}$. $ab = \sqrt[3]{4 - 3} = 1$. $x^3 = a^3 + b^3 + 3ab(a+b) = 4 + 3(1)x \implies x^3 - 3x = 4$.
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