Multiple choice

If the roots a quadratic equation x2 - x - 1 = 0 , are α and β , then find the value of α8 + β8 ?

  1. 47

  2. 54

  3. 59

  4. 68
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For x² - x - 1 = 0, we have α+β = 1 and αβ = -1. Using the recurrence α^n + β^n = (α+β)(α^{n-1} + β^{n-1}) - αβ(α^{n-2} + β^{n-2}), we build: α²+β² = 3, α^4+β^4 = 7, α^8+β^8 = 47. Therefore Option A (47) is correct. Options B, C, D (54, 59, 68) are incorrect.

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