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NDA2025MathematicsComplex NumberActual

If x + 1 x = 2 , then what is x^3 + 1 x^3 equal to?

Options

  1. A^3
  2. B3
  3. C2 3
  4. D3 3

Correct answer

C. 2 3

Step-by-step solution

Given x + 1 x = 2 Using the algebraic identity a^3 + b^3 = (a+b)^3 - 3ab(a+b) : x^3 + 1 x^3 = (x + 1 x )^3 - 3 (x + 1 x ) Substituting x + 1 x = 2 : x^3 + 1 x^3 = (2 )^3 - 3(2 ) x^3 + 1 x^3 = 8 ^3 - 6 x^3 + 1 x^3 = 2(4 ^3 - 3 ) Using the trigonometric identity 3 = 4 ^3 - 3 : x^3 + 1 x^3 = 2 3 Answer: 2 3

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