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

The text form of this sum (1/ (1+x^(b-a)+x^(c-a) )+(1/(1+x^(a-b)+x^(c-b) )+(1/(1+x^(b-c)+x^(a-c) )=1 is given below. So that students may not get confused with the text form of the sum.







Watch video or see this solution:
First term: (1/ (1+x^(b-a)+x^(c-a) )
=(1/ (1+x^b*x^a)+x^c*x^a))
=(x^a/ (x^a+x^b+x^c))
Second term: (1/ (1+x^(a-b)+x^(c-b) )
=(1/ (1+x^a*x^b)+x^c*x^b))
=(x^b/ (x^a+x^b+x^c))
Third term: (1/ (1+x^(b-c)+x^(a-c) )
=(1/ (1+x^b*x^c)+x^a*x^c))
=(x^c/ (x^a+x^b+x^c))
Therefore
First term+Second term+third term
=(x^a/ (x^a+x^b+x^c))+(x^b/ (x^a+x^b+x^c))+(x^c/ (x^a+x^b+x^c))
=((x^a+x^b+x^c)/ (x^a+x^b+x^c))
=1 
LHS=RHS
Proved
Its solution is also given in the video.
keywords:online mathematics, online mathematics degree, online mathematics courses, teaching mathematics.

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Comments

  1. simplify (2)^(1/3)*(3)^(1/4) Please solve this question

    ReplyDelete
    Replies
    1. (2^(1 / 3)) * (3^(1 / 4)) =
      1.65814935214
      This is the direct value.
      ============
      I think your some is incomplete.

      Delete

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