THE ANSWER IS : c) 6
RULE : nth roots of a complex no. are in G.P.
Given w as an imaginary root of 2.
Then the fifth roots of 2 may be put as 21/5, w, w2, w3, w4.
x = w + w2
Then x5 - 10x2 - 10x = (w + w2)5 - 10(w + w2)2 - 10(w + w2)
= (w5 + 5w6 + 10w7 + 10w8 + 5w9 + w10) - 10(w2 + 2w3 + w4) - 10(w + w2)
= (2 + 10w + 20w2 + 20w3 + 10w4 + 4) - (10w2 + 20w3 + 10w4) - (10w + 10w2)
= 6
So, what do you say ???
Moderation Team
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