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Railways PYQCBT 1 2016

RRB NTPC · Question 17

If (x2 - 4x + 1) = 0, then find the value of \(\frac{{{\rm{\;}}{x^3} + \frac{1}{{{x^3}}}}}{{{\rm{\;}}{x^2} + \frac{1}{{{x^2}}}}}\). A. 26/7 B. 13/7 C. 6/7 D. 33/7

  1. D

  2. A

  3. B

  4. C

Show answer & explanation

Answer: (B) A

Explanation

x² − 4x + 1 = 0 gives x + 1/x = 4. Then x² + 1/x² = 16 − 2 = 14 and x³ + 1/x³ = 4³ − 3 × 4 = 52. The ratio is 52/14 = 26/7.