CDS 2026 · PYQ · Algebra / Identities · medium
For the next two (02) items that follow:
16(x⁴ + 1/x⁴) - 257 = 0
What is (x² + 1/x²) equal to?
- A.25/16
- B.21/16
- C.19/4
- D.17/4✓ Correct
From 16(x⁴ + 1/x⁴) = 257, we get x⁴ + 1/x⁴ = 257/16. Now (x² + 1/x²)² = x⁴ + 2 + 1/x⁴ = 257/16 + 2 = 257/16 + 32/16 = 289/16. Therefore x² + 1/x² = √(289/16) = 17/4.
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