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CBSE Class 10 Answered

pls solve this math doubt

Asked by dhruvdilipschool | 07 Mar, 2022, 11:37: AM
Expert Answer
The three equations are:
1/a + 1/b + 1/a+x = 0  ... (i)
1/a + 1/c + 1/a+y = 0  ... (ii)
1/a + 1/x + 1/y = 0      ... (iii)
Using space equation space left parenthesis iii right parenthesis comma space we space get
1 over straight a equals negative 1 over straight x minus 1 over straight y equals negative fraction numerator open parentheses straight x plus straight y close parentheses over denominator xy end fraction
rightwards double arrow straight a equals negative fraction numerator xy over denominator straight x plus straight y end fraction space space space space... space left parenthesis 1 right parenthesis
Using space left parenthesis straight i right parenthesis space and space left parenthesis 1 right parenthesis comma space we space have
1 over straight b equals negative fraction numerator 1 over denominator straight a plus straight x end fraction minus 1 over straight a equals negative fraction numerator 1 over denominator negative begin display style fraction numerator xy over denominator straight x plus straight y end fraction end style plus straight x end fraction plus fraction numerator straight x plus straight y over denominator xy end fraction equals negative fraction numerator straight x plus straight y over denominator straight x squared end fraction plus fraction numerator straight x plus straight y over denominator xy end fraction equals fraction numerator open parentheses negative straight x minus straight y close parentheses xy plus straight x squared open parentheses straight x plus straight y close parentheses over denominator straight x cubed straight y end fraction
equals fraction numerator negative straight x squared straight y minus xy squared plus straight x cubed plus straight x squared straight y over denominator straight x cubed straight y end fraction
equals fraction numerator open parentheses straight x squared minus straight y squared close parentheses over denominator straight x squared straight y end fraction
rightwards double arrow straight b equals fraction numerator straight x squared straight y over denominator straight x squared minus straight y squared end fraction space space space space space... space left parenthesis 2 right parenthesis
Using space left parenthesis ii right parenthesis space and space left parenthesis 1 right parenthesis comma space we space have
1 over straight c equals negative fraction numerator 1 over denominator straight a plus straight y end fraction minus 1 over straight a equals negative fraction numerator 1 over denominator negative begin display style fraction numerator xy over denominator straight x plus straight y end fraction end style plus straight y end fraction plus fraction numerator straight x plus straight y over denominator xy end fraction equals negative fraction numerator straight x plus straight y over denominator straight y squared end fraction plus fraction numerator straight x plus straight y over denominator xy end fraction equals fraction numerator straight y squared minus straight x squared over denominator xy squared end fraction
rightwards double arrow straight c equals fraction numerator xy squared over denominator straight y squared minus straight x squared end fraction space space space space space... space left parenthesis 3 right parenthesis
Therefore comma
straight a plus straight b plus straight c equals negative fraction numerator xy over denominator straight x plus straight y end fraction plus fraction numerator straight x squared straight y over denominator straight x squared minus straight y squared end fraction plus fraction numerator xy squared over denominator straight y squared minus straight x squared end fraction equals fraction numerator negative xy open parentheses straight x minus straight y close parentheses plus straight x squared straight y minus xy squared over denominator straight x squared minus straight y squared end fraction
equals fraction numerator negative straight x squared straight y plus xy squared plus straight x squared straight y minus xy squared over denominator straight x squared minus straight y squared end fraction
equals 0
Answered by Renu Varma | 09 Mar, 2022, 11:21: AM
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