Archive
4th of April 2017
Mathematics
Q:

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

Kevin Menezes - CBSE - Class IX

Tuesday, April 04, 2017 at 09:22:AM

A:

Hi Kevin,

Check your Questions. The terms should be as follows. Check the second set of terms.

begin mathsize 16px style Consider comma space LHS
equals fraction numerator 1 over denominator 1 plus straight x to the power of left parenthesis straight b minus straight a right parenthesis end exponent plus straight x to the power of left parenthesis straight c minus straight a right parenthesis end exponent end fraction plus fraction numerator 1 over denominator 1 plus straight x to the power of bold left parenthesis bold a bold minus bold b bold right parenthesis end exponent plus straight x to the power of bold left parenthesis bold c bold minus bold b bold right parenthesis end exponent end fraction plus fraction numerator 1 over denominator 1 plus straight x to the power of left parenthesis straight b minus straight c right parenthesis end exponent plus straight x to the power of left parenthesis straight a minus straight c right parenthesis end exponent end fraction
equals fraction numerator 1 over denominator 1 plus straight x to the power of straight b straight x to the power of negative straight a end exponent plus straight x to the power of straight c straight x to the power of negative straight a end exponent end fraction plus fraction numerator 1 over denominator 1 plus straight x to the power of straight a straight x to the power of negative straight b end exponent plus straight x to the power of straight c straight x to the power of negative straight b end exponent end fraction plus fraction numerator 1 over denominator 1 plus straight x to the power of straight b straight x to the power of negative straight c end exponent plus straight x to the power of straight a straight x to the power of negative straight c end exponent end fraction
equals fraction numerator 1 over denominator 1 plus straight x to the power of negative straight a end exponent left parenthesis straight x to the power of straight b plus straight x to the power of straight c right parenthesis end fraction plus fraction numerator 1 over denominator 1 plus straight x to the power of negative straight b end exponent left parenthesis straight x to the power of straight a plus straight x to the power of straight c right parenthesis end fraction plus fraction numerator 1 over denominator 1 plus straight x to the power of negative straight c end exponent left parenthesis straight x to the power of straight b plus straight x to the power of straight a right parenthesis end fraction
equals fraction numerator 1 over denominator 1 plus begin display style fraction numerator straight x to the power of straight b plus straight x to the power of straight c over denominator straight x to the power of straight a end fraction end style end fraction plus fraction numerator 1 over denominator 1 plus begin display style fraction numerator straight x to the power of straight a plus straight x to the power of straight c over denominator straight x to the power of straight b end fraction end style end fraction plus fraction numerator 1 over denominator 1 plus begin display style fraction numerator straight x to the power of straight b plus straight x to the power of straight a over denominator straight x to the power of straight c end fraction end style end fraction
equals fraction numerator 1 over denominator fraction numerator straight x to the power of straight a plus straight x to the power of straight b plus straight x to the power of straight c over denominator straight x to the power of straight a end fraction end fraction plus fraction numerator 1 over denominator begin display style fraction numerator straight x to the power of straight b plus straight x to the power of straight a plus straight x to the power of straight c over denominator straight x to the power of straight b end fraction end style end fraction plus fraction numerator 1 over denominator begin display style fraction numerator straight x to the power of straight c plus straight x to the power of straight b plus straight x to the power of straight a over denominator straight x to the power of straight c end fraction end style end fraction
equals fraction numerator straight x to the power of straight a over denominator straight x to the power of straight a plus straight x to the power of straight b plus straight x to the power of straight c end fraction plus fraction numerator straight x to the power of straight b over denominator begin display style straight x to the power of straight a plus straight x to the power of straight b plus straight x to the power of straight c end style end fraction plus fraction numerator straight x to the power of straight c over denominator begin display style straight x to the power of straight a plus straight x to the power of straight b plus straight x to the power of straight c end style end fraction
equals fraction numerator straight x to the power of straight a plus straight x to the power of straight b plus straight x to the power of straight c over denominator straight x to the power of straight a plus straight x to the power of straight b plus straight x to the power of straight c end fraction
equals 1 equals RHS
Hence space proved. end style

Tuesday, April 04, 2017 at 12:14:PM