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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)`
2 years ago

```							Dear Piyush roots are  w and w2Remember1+ w + w2 = 0w3 = 11/w = w2    & 1/w2 = whence(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 RegardsArun (askIITians forum expert)
```
2 years ago
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