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Solve for x and y :b /ax + a/by = a2b2, x+y =2ab |
| Answer» {tex}\\frac { b x } { a } - \\frac { a y } { b } + a + b = 0{/tex}By taking L.C.M, we get{tex}\\frac { b ^ { 2 } x - a ^ { 2 } y + a ^ { 2 } b + b ^ { 2 } a } { a b } = 0{/tex}{tex}b^2x - a^2y = -a^2b - b^2a {/tex}.....(i){tex}bx - ay = -2ab{/tex} ..........(ii)Multiplying (i) by 1 and (ii) by a,we get{tex}b^2x - a^2y = -a^2b - b^2a{/tex} .......(iii){tex}abx - a^2y = -2a^2b{/tex} .........(iv)Subtracting (iii) from (iv){tex}(ab - b^2)x = -2a^2b + a^2b + ab^2{/tex}{tex}b(a - b)x = -a^2b + ab^2\xa0= -ab(a - b){/tex}{tex}\\therefore \\quad x = \\frac { - a b ( a - b ) } { b ( a - b ) }{/tex}x = -aPutting x = -a in (i), we getb2(-a) - a2y = -a2b\xa0- b2a-ab2\xa0- a2y = -a2b - b2a- a2y =-a2b - b2a +\xa0ab2{tex}- a ^ { 2 } y = - a ^ { 2 } b \\Rightarrow y = \\frac { - a ^ { 2 } b } { - a ^ { 2 } } = b{/tex}{tex}\\therefore{/tex}\xa0Solution is x = -a, y = b | |