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If x^2 + x + 1 = 0, then the value of (x + 1/x)^2 + (x^2 + 1/x^2) + .... + (x^27 + 1/x^27)2 is

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If x2 + x + 1 = 0, then the value of (x + 1/x)2 + (x2 + 1/x2) + .... + (x27 + 1/x27)2 is

(a)  27

(b)  72

(c)  54

(d)  None of these 

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Best answer

Correct option   (c)  54

Explanation:

∴ (ω + 1/ω)2 + (ω2 + 1/ω2) + (ω2 + 1/ω3)2 .....+ (ω27 + 1/ω27)2

= (–1)2 + (–1)2 + (2)2 + .................+(2)2

= 18 x 1 + 9 x 4 = 54

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