NDA 2025 · PYQ · Algebra · medium
If x² - x + 1 = 0, then what is (x - 1/x)² + (x - 1/x)⁴ + (x - 1/x)⁸ equal to?
- A.81
- B.85
- C.87✓ Correct
- D.90
From x² - x + 1 = 0, x + 1/x = 1 (dividing by x). Also x - 1/x: (x - 1/x)² = (x + 1/x)² - 4 = 1 - 4 = -3. So (x - 1/x)² = -3, (x - 1/x)⁴ = 9, (x - 1/x)⁸ = 81. Sum = -3 + 9 + 81 = 87.
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