Cuales son las raices de la ecuacion
mnx^2+mn=x(m^2+n^2)
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formamos una ecuación de la forma ax²+bx+c =0
para aplicar la formula general
![a=mn \\ b=-( m^{2} + n^{2}) \\ c= mn \\ \\ mn x^{2} -x( m^{2} + n^{2})+mn=
\\ formula
\\ \\ x=-b+- \frac{ \sqrt{ b^{2} -4ac} }{2a} =remplazamos
\\ \\ \frac{-.[-( m^{2} + n^{2})]+- \sqrt{-[-( m^{2} + n^{2})-4mn.mn } }{2mn} = \\ \\
\\ x = \frac{ m^{2} + n^{2} +- \sqrt{ [-( m^{2} + n^{2} )^{2} -4 m^{2} n^{2} } }{2mn}
\\ \\ x= \frac{ m^{2} + n^{2}+- \sqrt{ m^{4}+2 m^{2} n^{2} + n^{4} -4 m^{2} n^{2} } }{2mn}
\\ \\ [tex] \\ \\ x= \frac{ m^{2} + n^{2} +- \sqrt{ m^{4}-2 m^{2} n^{2} + n^{4} } }{2mn}
\\ \\
\\ \\ x= \frac{ m^{2} + n^{2} +- \sqrt{ ( m^{2} - n^{2}) ^{2} } }{2mn} = \\ \\
x= \frac{ m^{2} + n^{2}+-( m^{2} - n^{2} ) }{2mn} =
\\ \\ \frac{ m^{2} + n^{2} + m^{2} - n^{2} }{2mn} = \\ \\
x= \frac{2 m^{2} }{2mn} = \frac{m}{n} ..primera...respuesta
\\ \\ x= \frac{ m^{2} + n^{2}- m^{2} + n^{2} }{2mn} =
\\ \\ x= \frac{2 n^{2} }{2mn} = \frac{n}{m} ...segunda respuesta
\\ \\ saludos](https://tex.z-dn.net/?f=+a%3Dmn+%5C%5C+b%3D-%28+m%5E%7B2%7D+%2B+n%5E%7B2%7D%29+%5C%5C+c%3D+mn++%5C%5C+%5C%5C+++mn+x%5E%7B2%7D+-x%28+m%5E%7B2%7D+%2B+n%5E%7B2%7D%29%2Bmn%3D%0A+%5C%5C++formula%0A+%5C%5C++%5C%5C+x%3D-b%2B-+%5Cfrac%7B+%5Csqrt%7B+b%5E%7B2%7D+-4ac%7D+%7D%7B2a%7D++%3Dremplazamos%0A+%5C%5C++%5C%5C++%5Cfrac%7B-.%5B-%28+m%5E%7B2%7D+%2B+n%5E%7B2%7D%29%5D%2B-+%5Csqrt%7B-%5B-%28+m%5E%7B2%7D+%2B+n%5E%7B2%7D%29-4mn.mn+%7D++%7D%7B2mn%7D+%3D+%5C%5C++%5C%5C++%0A+%5C%5C+x+%3D++%5Cfrac%7B+m%5E%7B2%7D+%2B+n%5E%7B2%7D+%2B-+%5Csqrt%7B+%5B-%28+m%5E%7B2%7D+%2B+n%5E%7B2%7D+%29%5E%7B2%7D+-4+m%5E%7B2%7D++n%5E%7B2%7D+%7D+%7D%7B2mn%7D+%0A+%5C%5C++%5C%5C+x%3D++%5Cfrac%7B+m%5E%7B2%7D+%2B+n%5E%7B2%7D%2B-+%5Csqrt%7B+m%5E%7B4%7D%2B2+m%5E%7B2%7D++n%5E%7B2%7D+%2B+n%5E%7B4%7D+-4+m%5E%7B2%7D++n%5E%7B2%7D++%7D++%7D%7B2mn%7D+%0A+%5C%5C++%5C%5C%C2%A0%5Btex%5D+%5C%5C++%5C%5C+x%3D+++%5Cfrac%7B+m%5E%7B2%7D+%2B+n%5E%7B2%7D+%2B-+%5Csqrt%7B+m%5E%7B4%7D-2+m%5E%7B2%7D++n%5E%7B2%7D+%2B+n%5E%7B4%7D+%7D+%7D%7B2mn%7D%0A+%5C%5C++%5C%5C+%0A+%5C%5C++%5C%5C+x%3D+%5Cfrac%7B+m%5E%7B2%7D+%2B+n%5E%7B2%7D+%2B-+%5Csqrt%7B+%28+m%5E%7B2%7D+-+n%5E%7B2%7D%29+%5E%7B2%7D+%7D+%7D%7B2mn%7D+%3D+%5C%5C++%5C%5C+%0Ax%3D+++%5Cfrac%7B+m%5E%7B2%7D+%2B+n%5E%7B2%7D%2B-%28+m%5E%7B2%7D+-+n%5E%7B2%7D+%29+%7D%7B2mn%7D+%3D%0A+%5C%5C++%5C%5C++%5Cfrac%7B+m%5E%7B2%7D+%2B+n%5E%7B2%7D+%2B+m%5E%7B2%7D+-+n%5E%7B2%7D+%7D%7B2mn%7D+%3D+%5C%5C++%5C%5C+%0Ax%3D+%5Cfrac%7B2+m%5E%7B2%7D+%7D%7B2mn%7D+%3D+%5Cfrac%7Bm%7D%7Bn%7D+..primera...respuesta%0A+%5C%5C++%5C%5C+x%3D++%5Cfrac%7B+m%5E%7B2%7D+%2B+n%5E%7B2%7D-+m%5E%7B2%7D+%2B+n%5E%7B2%7D++%7D%7B2mn%7D+%3D%0A+%5C%5C++%5C%5C+x%3D+%5Cfrac%7B2+n%5E%7B2%7D+%7D%7B2mn%7D+%3D+%5Cfrac%7Bn%7D%7Bm%7D+...segunda+respuesta%0A+%5C%5C++%5C%5C+saludos "a=mn \\ b=-( m^{2} + n^{2}) \\ c= mn \\ \\ mn x^{2} -x( m^{2} + n^{2})+mn=
\\ formula
\\ \\ x=-b+- \frac{ \sqrt{ b^{2} -4ac} }{2a} =remplazamos
\\ \\ \frac{-.[-( m^{2} + n^{2})]+- \sqrt{-[-( m^{2} + n^{2})-4mn.mn } }{2mn} = \\ \\
\\ x = \frac{ m^{2} + n^{2} +- \sqrt{ [-( m^{2} + n^{2} )^{2} -4 m^{2} n^{2} } }{2mn}
\\ \\ x= \frac{ m^{2} + n^{2}+- \sqrt{ m^{4}+2 m^{2} n^{2} + n^{4} -4 m^{2} n^{2} } }{2mn}
\\ \\ [tex] \\ \\ x= \frac{ m^{2} + n^{2} +- \sqrt{ m^{4}-2 m^{2} n^{2} + n^{4} } }{2mn}
\\ \\
\\ \\ x= \frac{ m^{2} + n^{2} +- \sqrt{ ( m^{2} - n^{2}) ^{2} } }{2mn} = \\ \\
x= \frac{ m^{2} + n^{2}+-( m^{2} - n^{2} ) }{2mn} =
\\ \\ \frac{ m^{2} + n^{2} + m^{2} - n^{2} }{2mn} = \\ \\
x= \frac{2 m^{2} }{2mn} = \frac{m}{n} ..primera...respuesta
\\ \\ x= \frac{ m^{2} + n^{2}- m^{2} + n^{2} }{2mn} =
\\ \\ x= \frac{2 n^{2} }{2mn} = \frac{n}{m} ...segunda respuesta
\\ \\ saludos")
formamos una ecuación de la forma ax²+bx+c =0
para aplicar la formula general
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