solvefor x,(x+k)(x^2+3x-1)=x^3-x^2-13x+4

Solución

x, (x + k) (x^{2} + 3 x - 1) = x^{3} - x^{2} - 13 x + 4

x = \frac{- 3 + 13}{2}, x = - \frac{3 + 13}{2}; k \neq = - 4

Notación decimal

x = 0.30277 \dots, x = - 3.30277 \dots

Pasos de solución

(x + k) (x^{2} + 3 x - 1) = x^{3} - x^{2} - 13 x + 4

Desarrollar

(x + k) (x^{2} + 3 x - 1) : x^{3} + 3 x^{2} - x + k x^{2} + 3 k x - k

x^{3} + 3 x^{2} - x + k x^{2} + 3 k x - k = x^{3} - x^{2} - 13 x + 4

Restar

x^{3} - x^{2} - 13 x + 4

de ambos lados

x^{3} + 3 x^{2} - x + k x^{2} + 3 k x - k - (x^{3} - x^{2} - 13 x + 4) = x^{3} - x^{2} - 13 x + 4 - (x^{3} - x^{2} - 13 x + 4)

Simplificar

(k + 4) x^{2} + (3 k + 12) x - k - 4 = 0

Resolver con la fórmula general para ecuaciones de segundo grado:

x_{1, 2} = \frac{- ( 3 k + 12 ) \pm ( 3 k + 12 ) ^{2} - 4 ( k + 4 ) ( - k - 4 )}{2 ( k + 4 )}

Simplificar

(3 k + 12)^{2} - 4 (k + 4) (- k - 4) : 13 (k + 4)

x_{1, 2} = \frac{- ( 3 k + 12 ) \pm 13 ( k + 4 )}{2 ( k + 4 )}; k \neq = - 4

Separar las soluciones

x_{1} = \frac{- ( 3 k + 12 ) + 13 ( k + 4 )}{2 ( k + 4 )}, x_{2} = \frac{- ( 3 k + 12 ) - 13 ( k + 4 )}{2 ( k + 4 )}

x = \frac{- ( 3 k + 12 ) + 13 ( k + 4 )}{2 ( k + 4 )} : \frac{- 3 + 13}{2}

x = \frac{- ( 3 k + 12 ) - 13 ( k + 4 )}{2 ( k + 4 )} : - \frac{3 + 13}{2}

Las soluciones a la ecuación de segundo grado son:

x = \frac{- 3 + 13}{2}, x = - \frac{3 + 13}{2}; k \neq = - 4

m + 3 = m^{2} - 4 m - 3

16 y^{2} - 1 = 0

x^{2} - \frac{2}{3} x + \frac{1}{12} = 0

8 x^{2} + 4 x - 4 = 0

12 x^{2} + 57 x + 45 = 0