CTET PAPER II 2021 · PYQ · Algebraic Identities · hard
If x⁴ + 1/x⁴ = 322, x ≠ 0, then one of the values of (x − 1/x) is
- A.2
- B.4✓ Correct
- C.6
- D.8
Given x⁴ + 1/x⁴ = 322. We know x⁴ + 1/x⁴ = (x² + 1/x²)² − 2, so (x² + 1/x²)² = 324, giving x² + 1/x² = 18. Also (x − 1/x)² = x² − 2 + 1/x² = 18 − 2 = 16, so x − 1/x = ±4. One value is 4.
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