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| 1. |
Solve xy/x+y=1/5 , xy/x+y =1/7 |
| Answer» {tex}\\frac{xy}{x + y}{/tex}\xa0=\xa0{tex}\\frac{1}{5}{/tex}\xa0{tex}\\Rightarrow{/tex}\xa0{tex}\\frac{x + y}{xy}{/tex}\xa0=\xa0{tex}\\frac{5}{1}{/tex}{tex}\\Rightarrow{/tex}{tex}\\frac{1}{y}{/tex}+\xa0{tex}\\frac{1}{x}{/tex}\xa0{tex}= 5{/tex}....(i)and\xa0{tex}\\frac{xy}{x - y}{/tex}\xa0=\xa0{tex}\\frac{1}{7}{/tex}\xa0{tex}\\Rightarrow{/tex}\xa0{tex}\\frac{x - y}{xy}{/tex}\xa0{tex}= 7{/tex}{tex}\\Rightarrow{/tex}\xa0{tex}\\frac{1}{y}{/tex}\xa0-\xa0{tex}\\frac{1}{x}{/tex}\xa0= 7...(ii)Now solve equation (i) and (ii) by assuming {tex}\\frac{1}{y}{/tex}\xa0{tex}= a{/tex} and\xa0{tex}\\frac{1}{x}{/tex}\xa0{tex}= b{/tex}{tex}\\therefore{/tex} eq.(i) and (ii) becomes{tex}\\Rightarrow{/tex}{tex}b = -1{/tex}.....(iii)Putting the value of\xa0{tex} b = -1{/tex}\xa0from\xa0eq. (iii) in equation (i), we get{tex}a - 1 = 5{/tex}\xa0{tex}\\Rightarrow{/tex}\xa0{tex}a = 6{/tex}Now,\xa0{tex}\\frac{1}{y}{/tex}\xa0{tex}= 6{/tex}\xa0{tex}\\Rightarrow{/tex}\xa0{tex}y ={/tex}\xa0{tex}\\frac{1}{6}{/tex}and\xa0{tex}\\frac{1}{x}{/tex}\xa0= -1\xa0{tex}\\Rightarrow{/tex}\xa0{tex}x = -1{/tex} | |