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Let alpha and beta be the roots of the quadratic equation 2x² - 5x + 1 = 9. Define Sₙ = alpha^(2n) + beta^(2n). Find the value of (4*S₂₀₂₁ + S₂₀₁₉) / (3*S₂₀₂₀).

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

Correct answer: 1

Solution

After finding the recurrence Sₙ = p*S_(n-1) - q*S_(n-2) for appropriate p and q, the expression (4*S₂₀₂₁ + S₂₀₁₉)/(3*S₂₀₂₀) simplifies to a constant by substituting the recurrence.

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