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1+x+x^2=a(1+x)+b(1+x^2)+c(x+x^2)

Solución

1 + x + x^{2} = a (1 + x) + b \cdot (1 + x^{2}) + c \cdot (x + x^{2})

Solución

x = \frac{- 1 + c + a + a ^{2} + 2 a - 4 ab - 2 a c + 8 b + c ^{2} + 2 c - 4 b ^{2} - 4 b c - 3}{2 ( 1 - c - b )}, x = \frac{- 1 + c + a - a ^{2} + 2 a - 4 ab - 2 a c + 8 b + c ^{2} + 2 c - 4 b ^{2} - 4 b c - 3}{2 ( 1 - c - b )}; 1 - c - b \neq = 0

Pasos de solución

1 + x + x^{2} = a (1 + x) + b (1 + x^{2}) + c (x + x^{2})

Desarrollar

a (1 + x) + b (1 + x^{2}) + c (x + x^{2}) : a + a x + b + b x^{2} + c x + c x^{2}

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

Mover

c x^{2}

al lado izquierdo

1 + x + x^{2} - c x^{2} = a + a x + b + b x^{2} + c x

Mover

c x

al lado izquierdo

1 + x + x^{2} - c x^{2} - c x = a + a x + b + b x^{2}

Mover

b x^{2}

al lado izquierdo

1 + x + x^{2} - c x^{2} - c x - b x^{2} = a + a x + b

Mover

b

al lado izquierdo

1 + x + x^{2} - c x^{2} - c x - b x^{2} - b = a + a x

Restar

a + a x

de ambos lados

1 + x + x^{2} - c x^{2} - c x - b x^{2} - b - (a + a x) = a + a x - (a + a x)

Simplificar

(1 - c - b) x^{2} + (1 - c - a) x + 1 - b - a = 0

Resolver con la fórmula general para ecuaciones de segundo grado:

x_{1, 2} = \frac{- ( 1 - c - a ) \pm ( 1 - c - a ) ^{2} - 4 ( 1 - c - b ) ( 1 - b - a )}{2 ( 1 - c - b )}

Simplificar

(1 - c - a)^{2} - 4 (1 - c - b) (1 - b - a) : a^{2} + 2 a - 4 ab - 2 a c + 8 b + c^{2} + 2 c - 4 b^{2} - 4 b c - 3

x_{1, 2} = \frac{- ( 1 - c - a ) \pm a ^{2} + 2 a - 4 ab - 2 a c + 8 b + c ^{2} + 2 c - 4 b ^{2} - 4 b c - 3}{2 ( 1 - c - b )}; 1 - c - b \neq = 0

Separar las soluciones

x_{1} = \frac{- ( 1 - c - a ) + a ^{2} + 2 a - 4 ab - 2 a c + 8 b + c ^{2} + 2 c - 4 b ^{2} - 4 b c - 3}{2 ( 1 - c - b )}, x_{2} = \frac{- ( 1 - c - a ) - a ^{2} + 2 a - 4 ab - 2 a c + 8 b + c ^{2} + 2 c - 4 b ^{2} - 4 b c - 3}{2 ( 1 - c - b )}

x = \frac{- ( 1 - c - a ) + a ^{2} + 2 a - 4 ab - 2 a c + 8 b + c ^{2} + 2 c - 4 b ^{2} - 4 b c - 3}{2 ( 1 - c - b )} : \frac{- 1 + c + a + a ^{2} + 2 a - 4 ab - 2 a c + 8 b + c ^{2} + 2 c - 4 b ^{2} - 4 b c - 3}{2 ( 1 - c - b )}

x = \frac{- ( 1 - c - a ) - a ^{2} + 2 a - 4 ab - 2 a c + 8 b + c ^{2} + 2 c - 4 b ^{2} - 4 b c - 3}{2 ( 1 - c - b )} : \frac{- 1 + c + a - a ^{2} + 2 a - 4 ab - 2 a c + 8 b + c ^{2} + 2 c - 4 b ^{2} - 4 b c - 3}{2 ( 1 - c - b )}

Las soluciones a la ecuación de segundo grado son:

x = \frac{- 1 + c + a + a ^{2} + 2 a - 4 ab - 2 a c + 8 b + c ^{2} + 2 c - 4 b ^{2} - 4 b c - 3}{2 ( 1 - c - b )}, x = \frac{- 1 + c + a - a ^{2} + 2 a - 4 ab - 2 a c + 8 b + c ^{2} + 2 c - 4 b ^{2} - 4 b c - 3}{2 ( 1 - c - b )}; 1 - c - b \neq = 0

Ejemplos populares

solvefor x,16x^2-24xy+9y^2-30x-40y=0 resolver para

x, 16 x^{2} - 24 x y + 9 y^{2} - 30 x - 40 y = 0

2 x^{2} - 3 x + 20 = 0

x^{2} - 3 x - 7 = 3

- 9 y^{2} + 24 = 0

x^{2} = 100