solvefor y,m=y^2-(y^1)/(x^2)-x^1

Solución

resolver para

y, m = y^{2} - \frac{y ^{1}}{x ^{2}} - x^{1}

y = \frac{1 + 1 - 4 x ^{2} ( - x ^{3} - m x ^{2} )}{2 x ^{2}}, y = \frac{1 - 1 - 4 x ^{2} ( - x ^{3} - m x ^{2} )}{2 x ^{2}}; x \neq = 0

Pasos de solución

m = y^{2} - \frac{y ^{1}}{x ^{2}} - x^{1}

Multiplicar ambos lados por

x^{2}

m x^{2} = y^{2} x^{2} - y - x^{3}; x \neq = 0

Intercambiar lados

y^{2} x^{2} - y - x^{3} = m x^{2}; x \neq = 0

Mover

m x^{2}

al lado izquierdo

y^{2} x^{2} - y - x^{3} - m x^{2} = 0; x \neq = 0

Escribir en la forma binómica

a x^{2} + b x + c = 0

x^{2} y^{2} - y - x^{3} - m x^{2} = 0; x \neq = 0

Resolver con la fórmula general para ecuaciones de segundo grado:

y_{1, 2} = \frac{- ( - 1 ) \pm ( - 1 ) ^{2} - 4 x ^{2} ( - x ^{3} - m x ^{2} )}{2 x ^{2}}

Simplificar

(- 1)^{2} - 4 x^{2} (- x^{3} - m x^{2}) : 1 - 4 x^{2} (- x^{3} - m x^{2})

y_{1, 2} = \frac{- ( - 1 ) \pm 1 - 4 x ^{2} ( - x ^{3} - m x ^{2} )}{2 x ^{2}}; x \neq = 0

Separar las soluciones

y_{1} = \frac{- ( - 1 ) + 1 - 4 x ^{2} ( - x ^{3} - m x ^{2} )}{2 x ^{2}}, y_{2} = \frac{- ( - 1 ) - 1 - 4 x ^{2} ( - x ^{3} - m x ^{2} )}{2 x ^{2}}

y = \frac{- ( - 1 ) + 1 - 4 x ^{2} ( - x ^{3} - m x ^{2} )}{2 x ^{2}} : \frac{1 + 1 - 4 x ^{2} ( - x ^{3} - m x ^{2} )}{2 x ^{2}}

y = \frac{- ( - 1 ) - 1 - 4 x ^{2} ( - x ^{3} - m x ^{2} )}{2 x ^{2}} : \frac{1 - 1 - 4 x ^{2} ( - x ^{3} - m x ^{2} )}{2 x ^{2}}

Las soluciones a la ecuación de segundo grado son:

y = \frac{1 + 1 - 4 x ^{2} ( - x ^{3} - m x ^{2} )}{2 x ^{2}}, y = \frac{1 - 1 - 4 x ^{2} ( - x ^{3} - m x ^{2} )}{2 x ^{2}}; x \neq = 0

x, z^{2} + 4 y^{2} - 4 x^{2} = 0

3 r^{2} = 4 r - 1

z^{2} + 4 z + 1 = 0

x^{2} + 7 x - 9 = 0

(x + 5) (2 x - 1) = 0