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For (x>1), what is the sum of the coefficients of all terms with odd degree in the expansion of (x+√(x³-1))⁵+(x-√(x³-1))⁵?

1. 0
2. 1
3. 2
4. -1

Correct answer: 2

Solution

(x+sqrt(x^3-1))^5 + (x-sqrt(x^3-1))^5 = 10x^7 + 20x^6 + 2x^5 - 20x^4 - 20x^3 + 10x. The odd-degree coefficients are 10 (x^7) + 2 (x^5) - 20 (x^3) + 10 (x^1) = 2.

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