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ICSE Class 9 Answered

If  abc = 1;  then show that:
 
fraction numerator 1 over denominator 1 plus a plus b to the power of negative 1 end exponent end fraction space plus space fraction numerator 1 over denominator 1 plus b plus c to the power of negative 1 end exponent end fraction space plus space fraction numerator 1 over denominator 1 plus c plus a to the power of negative 1 end exponent end fraction space equals space 1
Asked by Ashwin Kumar | 09 Feb, 2015, 07:17: PM
answered-by-expert Expert Answer
G i v e n space t h a t space a b c equals 1 C o n s i d e r space t h e space l e f t space h a n d space s i d e space e x p r e s s i o n colon fraction numerator 1 over denominator 1 plus a plus b to the power of negative 1 end exponent end fraction plus fraction numerator 1 over denominator 1 plus b plus c to the power of negative 1 end exponent end fraction plus fraction numerator 1 over denominator 1 plus c plus a to the power of negative 1 end exponent end fraction equals fraction numerator 1 over denominator 1 plus a plus begin display style 1 over b end style end fraction plus fraction numerator 1 over denominator 1 plus b plus c to the power of negative 1 end exponent end fraction plus fraction numerator 1 over denominator 1 plus c plus a to the power of negative 1 end exponent end fraction equals fraction numerator b over denominator b plus a b plus 1 end fraction plus fraction numerator 1 over denominator 1 plus b plus a b end fraction plus fraction numerator 1 over denominator 1 plus c plus a to the power of negative 1 end exponent end fraction equals fraction numerator b plus 1 over denominator b plus a b plus 1 end fraction plus fraction numerator 1 over denominator 1 plus c plus b c end fraction equals fraction numerator b plus 1 over denominator b plus begin display style 1 over c end style plus 1 end fraction plus fraction numerator 1 over denominator 1 plus c plus b c end fraction equals fraction numerator c open parentheses b plus 1 close parentheses over denominator b c plus c plus 1 end fraction plus fraction numerator 1 over denominator 1 plus c plus b c end fraction equals fraction numerator b c plus c over denominator b c plus c plus 1 end fraction plus fraction numerator 1 over denominator 1 plus c plus b c end fraction equals fraction numerator b c plus c plus 1 over denominator b c plus c plus 1 end fraction equals 1
Answered by Vimala Ramamurthy | 10 Feb, 2015, 11:01: AM
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