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Solve for x: (x - 1)⁴ + (x - 5)⁴ = 82.

1. x = 2 and x = 4
2. x = 1 and x = 5
3. x = 0 and x = 6
4. x = 3 +/- sqrt(2)

Correct answer: x = 2 and x = 4

Solution

Centring at the midpoint x = 3 turns the equation into an even (biquadratic) equation in y, which factors into a quadratic in y² with one usable (non-negative) root.

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