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X-a/x-b + x-b/x-a =a/b + b/a solve the quadratic equation |
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Answer» {tex}{{x - a} \\over {x - b}} + {{x - b} \\over {x - a}} = {a \\over b} + {b \\over a}{/tex}=> {tex}{{{x^2} + {a^2} - 2ax + {x^2} + {b^2} - 2bx} \\over {{x^2} - ax - bx + ab}} = {{{a^2} + {b^2}} \\over {ab}}{/tex}=> {tex}{{2{x^2} + {a^2} - 2ax + {b^2} - 2bx} \\over {{x^2} - ax - bx + ab}} = {{{a^2} + {b^2}} \\over {ab}}{/tex}=> {tex}2ab{x^2} + {a^3}b - 2{a^2}bx + a{b^3} - 2a{b^2}x = {a^2}{x^2} - {a^3}x - {a^2}bx + {a^3}b + {b^2}{x^2} - a{b^2}x - {b^3}x + a{b^3}{/tex}=> {tex}2ab{x^2} - {a^2}bx - a{b^2}x = {a^2}{x^2} - {a^3}x + {b^2}{x^2} - {b^3}x{/tex}=> {tex}{a^2}{x^2} - 2ab{x^2} + {b^2}{x^2} - {a^3}x - {b^3}x + {a^2}bx + a{b^2}x = 0{/tex}=> {tex}{x^2}\\left( {{a^2} + {b^2} - 2ab} \\right)+x\\left( { - {a^3} - {b^3} + {a^2}b + a{b^2}} \\right) = 0{/tex}=> {tex}x\\left[ {x\\left( {{a^2} + {b^2} - 2ab} \\right) + \\left( { - {a^3} - {b^3} + {a^2}b + a{b^2}} \\right)} \\right] = 0{/tex}=> {tex}x = 0{/tex}\xa0Or\xa0{tex}x = {{{a^3} + {b^3} - {a^2}b - a{b^2}} \\over {{{\\left( {a - b} \\right)}^2}}}{/tex} x - a /x - b + x - b / x - a = a/b + b/ax2 + a2 - 2ax + x2 + b2 - 2bx /x2 + ab -ax - bx = a2 + b2 /ab |
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