If x^2+x+1=0 then find the value of (X+1/x)^2+ (x^2+1/x^2)+(x^3+1/x^3)^2+................(x^27+1/x^27) I have attached the image of the question. (HINT: maybe it`s related to come Roots of unity)

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Arun · Answer

Dear Piyush roots are w and w 2 Remember 1+ w + w 2 = 0 w 3 = 1 1/w = w 2 & 1/w 2 = w hence (w + 1/w) 2 + (w 2 + 1/w 2 ) 2 + (w 3 + 1/w 3 ) 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)

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If x^2+x+1=0 then find the value of (X+1/x)^2+ (x^2+1/x^2)+(x^3+1/x^3)^2+................(x^27+1/x^27) I have attached the image of the question. (HINT: maybe it`s related to come Roots of unity)

If x^2+x+1=0 then find the value of (X+1/x)^2+ (x^2+1/x^2)+(x^3+1/x^3)^2+................(x^27+1/x^27) I have attached the image of the question. (HINT: maybe it`s related to come Roots of unity)

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If x^2+x+1=0 then find the value of (X+1/x)^2+ (x^2+1/x^2)+(x^3+1/x^3)^2+................(x^27+1/x^27) I have attached the image of the question. (HINT: maybe it`s related to come Roots of unity)

If x^2+x+1=0 then find the value of (X+1/x)^2+ (x^2+1/x^2)+(x^3+1/x^3)^2+................(x^27+1/x^27) I have attached the image of the question. (HINT: maybe it`s related to come Roots of unity)

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Other Related Questions on Magical Mathematics[Interesting Approach]

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