Multiple choice

Directions: Solve the following question and mark the best possible option. If x + 1 = x2 and x > 0, then 2x4 is

  1. 6 + 4 5

  2. 3 + 5 5

  3. 5 + 3 5

  4. 7 + 3 5
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D Correct answer
AI explanation

Using the quadratic formula for x^2 - x - 1 = 0 gives x = (1 + sqrt(5)) / 2 since x > 0. From the original equation, x^2 = x + 1, so x^4 = (x + 1)^2 = x^2 + 2x + 1. Substituting x + 1 for x^2 yields x^4 = 3x + 2, making 2x^4 = 6x + 4, which equals 3(1 + sqrt(5)) + 4. This simplifies to 7 + 3 * sqrt(5).

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