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If a+b+c=0, prove that: 1/(a+x^a+x^-b)+1/(a+x^b+x^-c)+1/(1+x^c+x^-a)

If a+b+c=0,
prove that:
1/(a+x^a+x^-b)+1/(a+x^b+x^-c)+1/(1+x^c+x^-a)

Grade:9

1 Answers

Arun
25763 Points
2 years ago
Dear Ayush
 
Reverse Proof-
 
  1/(x^b + x^(-c) + 1) + 1/(x^c+ x^(-a)+1) + 1/ (x^a + x^(-b) + 1) = 1 

1/(x^b + x^(-c) + 1) + 1/(x^c+ x^(-a)+1) + 1/ (x^a + x^(-b) + 1) - 1 = 0 

[x^(a+b+c) - 1]^2/[(x^(a + b) + x^b +1) (x^(a + c) + x^a + 1) (x^(b + c) + x^c + 1)] = 0 

x^(a + b + c) = 1 

a + b + c = 0

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