Arun
Last Activity: 7 Years ago
Dear Piyush
roots are w and w2
Remember
1+ w + w2 = 0
w3 = 1
1/w = w2 & 1/w2 = w
hence
(w + 1/w)2 + (w2 + 1/w2)2 + (w3 + 1/w3)2 ….....
now
(w + w^2)^2 + (w^2 + w)^2 + 2^2 + (w + w^2)^2 + (w^2 + w)^2 + 2^2 + …....
= ( – 1)2 + ( –1)2 + 4 + ( – 1)2 + ( –1)2 + 4+( – 1)2 + ( –1)2 + 4+( – 1)2 + ( –1)2 + 4+( – 1)2 + ( –1)2 + 4+( – 1)2 + ( –1)2 + 4+( – 1)2 + ( –1)2 + 4+( – 1)2 + ( –1)2 + 4+( – 1)2 + ( –1)2 + 4
= 36 + 18
= 54
Regards
Arun (askIITians forum expert)
