Multiple choice

If a and ß are the roots of the equation x2- x - 1 = 0, then what is the value of (a4 +ß4 )?

  1. 7

  2. 0

  3. 2

  4. None of the above

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A Correct answer
Explanation

For x² - x - 1 = 0, sum a + ß = 1 and product aß = -1. First find a² + ß² = (a + ß)² - 2aß = 1 + 2 = 3. Then a⁴ + ß⁴ = (a² + ß²)² - 2(aß)² = 9 - 2 = 7.