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If x^2+x+1=0 then prove that (x+1/x)^2+(x^2+1/x^2)^2.........+(x^27+1/x^27)^2=54

If x^2+x+1=0 then prove that (x+1/x)^2+(x^2+1/x^2)^2.........+(x^27+1/x^27)^2=54

Grade:12

1 Answers

Sourabh Singh IIT Patna
askIITians Faculty 2104 Points
5 years ago
the result of the equation x^2+x+1=0 are the cuberoots of unity use that in the expression
you can write x+1/x = -1.Use this and you will get the answer

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