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If Sₖ = a^k + b^k + c^k, then the determinant Δ = [S₀, S₁, S₂; S₁, S₂, S₃; S₂, S₃, S₄] is equal to:

1. S₆
2. S₅ - S₃
3. S₆ - S₄
4. None of these

Correct answer: None of these

Solution

This is the symmetric-function (Hankel) determinant, which evaluates to ((a-b)(b-c)(c-a))^2. This equals none of S6, S5-S3, or S6-S4, so the answer is None of these.

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