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Let P = (2 + sqrt(3))⁵ and let f = P - [P], where [P] denotes the greatest integer not exceeding P. Find the value of f²/(1 - f) - 720.

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

Correct answer: 2

Solution

P + Q = 724 (integer), so [P] = 723 and f = P - 723. Since Q = 1 - f and P*Q = 1, we get f² = 722*Q, so f²/(1-f) = f²/Q = 722. Thus 722 - 720 = 2.

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