GATE AG 2018 • Q9 MCQ • 2 Marks

Section 8: General Aptitude

Quantitative Aptitude

Subtopic: Ratios & Percentages

Question Statement:

If x² + x − 1 = 0, what is the value of x⁴ + 1/x⁴ ?

Options:

  • (A) 1
  • (B) 5
  • (C) 7
  • (D) 9

Official Answer Key:

C

Step-by-Step Solution & Explanation

Divide x² + x − 1 = 0 by x: x + 1 − 1/x = 0 ⇒ x − 1/x = −1. x² + 1/x² = (x − 1/x)² + 2 = 1 + 2 = 3. x⁴ + 1/x⁴ = (x² + 1/x²)² − 2 = 9 − 2 = 7. Distractor (D) 9 is (x² + 1/x²)² without subtracting 2.

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