Let α and β be the roots of the equation x 2 - x - 1 = 0 . If p k = α k + β k , k ≥ 1 , then which one of the following statements is not true?

Question

Let α and β be the roots of the equation x 2 - x - 1 = 0 . If p k = α k + β k , k ≥ 1 , then which one of the following statements is not true?, p 3 = p 5 - p 4, p 5 = 11, p 1 + p 2 + p 3 + p 4 + p 5 = 26, p 5 = p 2 ⋅ p 3

MARKS App · Accepted Answer

α 5 = 5 α + 3 β 5 = 5 β + 3 P 5 = 5 α + β + 6 = 5 1 + 6 P 5 = 11 and P 2 = α 2 + β 2 = α + 1 + β + 1 = 3 and P 3 = α 3 + β 3 = 2 α + 1 + 2 β + 1 = 2 1 + 2 = 4 P 2 × P 3 = 12 and P 5 = 11 ⇒ P 5 ≠ P 2 × P 3

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