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Let alpha , beta and gamma be the roots ...

Let `alpha , beta` and `gamma` be the roots of the equation `x^3 - x - 1 = 0 `. If `P_k = (alpha)^k + (beta)^k + (gamma)^k , k gt= 1` , then which one of the following statements is not true?

A

`P_3 = P_1+P_2 + 1`

B

`P_2 = P_4`

C

`P_5 = P_6`

D

`P_5 = P_3`

Text Solution

Verified by Experts

The correct Answer is:
D
According to given the equation `P_(k+3) = P_(k+1) +P_k` and `P_1 = 0, P_2 = 2, P_3 = 3`
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