11since. alpha and beta are the roots of x2+px+q=0, therefore alpha +beta =-p ........(1)
satisfying alpha and beta in second equation and subtracting the two equations we get
alpha2n- beta 2n+pn(alphan-betan)=0
therefore
alphan+betan=-pn...(2)
satisfying alpha/ beta in its equation we get
alphan+betan+(alpha+beta)n=0
-pn+(-p)n=0
from (1) and (2) we get
-pn+(-1)npn=0
this is true only if n is an even integer.