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Asked by deepakiitian2004 | 04 Jan, 2022, 08:35: PM
Expert Answer
Given: a + {1/(b + {1/c+1})} = 24/5straight a plus fraction numerator 1 over denominator straight b plus begin display style fraction numerator 1 over denominator straight c plus 1 end fraction end style end fraction equals 24 over 5
Now comma space 24 over 5 space equals space 4 plus 4 over 5 space equals space 4 plus fraction numerator 1 over denominator begin display style 5 over 4 end style end fraction space equals space 4 plus fraction numerator 1 over denominator 1 plus begin display style 1 fourth end style end fraction space equals space 4 plus fraction numerator 1 over denominator 1 plus begin display style fraction numerator 1 over denominator 3 plus 1 end fraction end style end fraction
Therefore comma space straight a plus fraction numerator 1 over denominator straight b plus begin display style fraction numerator 1 over denominator straight c plus 1 end fraction end style end fraction space equals space space 4 plus fraction numerator 1 over denominator 1 plus begin display style fraction numerator 1 over denominator 3 plus 1 end fraction end style end fraction
Comparing space the space two space sides comma space we space get
straight a equals 4 comma space straight b equals 1 space and space straight c equals 3
Thus comma space straight a plus straight b plus straight c equals 8
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