Ok, I can't seem to be able to prove this one, a litle help would be good
parts 1 and 2 are ok, but you need them for 3) (nb, * is pie)
p(x) = x^6 + x^3 + 1
1. show roots of p(x)=0 are amongst x^9 - 1 = 0
2. Show p(x) = (x^2 -2xcos2*/9 + 1)(x^2 -2xcos4*/9 + 1)(x^2 -2xcos8*/9 + 1)
3. (cant get it)
hence show
cos2*/9.cos4*/9 + cos4*/9.cos8*/9 + cos8*/9cos2*/9 = -3/4
thanks a lot
parts 1 and 2 are ok, but you need them for 3) (nb, * is pie)
p(x) = x^6 + x^3 + 1
1. show roots of p(x)=0 are amongst x^9 - 1 = 0
2. Show p(x) = (x^2 -2xcos2*/9 + 1)(x^2 -2xcos4*/9 + 1)(x^2 -2xcos8*/9 + 1)
3. (cant get it)
hence show
cos2*/9.cos4*/9 + cos4*/9.cos8*/9 + cos8*/9cos2*/9 = -3/4
thanks a lot