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

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),kge1`, 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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