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IF A1,A2,A3,...,A(N-1) BE N-TH ROOTS OF THE UNITY THEN THE VALUE OF (A1/3-A1+A2/3-A2+A3/3-A3+...+A(N-1)/3-A(N-1))= A)N/3 N-1 B)N-1/3 N-1

IF A1,A2,A3,...,A(N-1) BE N-TH ROOTS OF THE UNITY THEN THE VALUE OF (A1/3-A1+A2/3-A2+A3/3-A3+...+A(N-1)/3-A(N-1))=


A)N/3N-1 


B)N-1/3N-1 

Grade:11

1 Answers

shaswat roy
19 Points
9 years ago

we know that  (x-1)(x-A1)(x-A2)...(x-A(N-1)) = x^n - 1

the denominator of LHS is 1 you can write 1 as A1.A2.A3.A4....A(N-1)

now you only have to do some arrangin take log on both sides,differentiate wrt x and put x=3.

u'll get the ans.

good luck

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