Let α and β be the roots of the equation x2−x−1=0. If pk=(α)k+(β)k,k≥1, then which one of the following statements is not true?

It is given that α and β are roots of quadratic equation x2 - x - 1=0, so sum of roots = α + 0 = 1, and product of roots ==αβ=−1and pk=αk+βk,k≥1so, p1=α+β=1p2=α2+β2=(α+β)2−2αβ=1+2=3 p3=α3+β3=(α+β)3−3αβ(α+β)=1+3=4 p4=α4+β4=(α+β)4−4αβα2+β2−6α2β2 =1+12−6=7and p5=α5+β5 =(α+β)5−5αβα3+β3−10α2β2(α+β) =1+20−10=11 ∵  p3=p5-p4=4 p1+p2+p3+p4+p5=1+3+4+7+11=26  but p5≠p2·p3