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| 1. |
(X+Y)/XY= 2 ,(X-Y)/XY=6 solve by cross multiplication method |
| Answer» {tex}{{x + y} \\over {xy}} = 2{/tex} => {tex}{1 \\over x} + {1 \\over y} = 2{/tex} => {tex}p + q = 2{/tex} .....(i) [Let\xa0{tex}p = {1 \\over x},q = {1 \\over y}{/tex}]And {tex}{{x - y} \\over {xy}} = 6{/tex} => {tex}{1 \\over x} - {1 \\over y} = 6{/tex} => {tex}p -q = 6{/tex} .....(ii) [Let\xa0{tex}p = {1 \\over x},q = {1 \\over y}{/tex}]{tex}{p\\over {{b_1}{c_2} - {b_2}{c_1}}} = {q \\over {{c_1}{a_2} - {c_2}{a_1}}} = {{ - 1} \\over {{a_1}{b_2} - {a_2}{b_1}}}{/tex}=> {tex}{p \\over {1 \\times 6 - \\left( { - 1} \\right) \\times 2}} = {q \\over {2 \\times 1 - 6 \\times 1}} = {{ - 1} \\over {1 \\times \\left( { - 1} \\right) - 1 \\times 1}}{/tex}=> {tex}{p \\over 8} = {q \\over { - 4}} = {{ - 1} \\over { - 2}}{/tex}Taking {tex}{p \\over 8} = {1 \\over 2}{/tex} => {tex}p = 4{/tex}Taking\xa0{tex}{q \\over { - 4}} = {1 \\over 2}{/tex} => {tex}q = - 2{/tex}{tex}4 = {1 \\over x}, - 2 = {1 \\over y}{/tex} => {tex}x = {1 \\over 4},y = {{ - 1} \\over 2}{/tex} | |