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If the coefficient of x⁷ in the expansion of ax² + (1/bx)¹¹ is equal to the coefficient of x^−7 in [ax − (1/bx²)]¹¹, then the parameters a and b must satisfy which relation?

1. a − b = 1
2. a + b = 1
3. a/b = 1
4. ab = 1

Correct answer: ab = 1

Solution

The coefficients of x⁷ and x^−7 in the given expressions must be equal, which leads to the relationship ab = 1. This indicates that the product of the parameters a and b must equal 1 for the coefficients to match.

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