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(2x+5)^6=(1-x)^6

Solución

(2 x + 5)^{6} = (1 - x)^{6}

Solución

x = - 6, x = - \frac{4}{3}

+1

Notación decimal

x = - 6, x = - 1.33333 \dots

Pasos de solución

(2 x + 5)^{6} = (1 - x)^{6}

Desarrollar

(2 x + 5)^{6} : 64 x^{6} + 960 x^{5} + 6000 x^{4} + 20000 x^{3} + 37500 x^{2} + 37500 x + 15625

Desarrollar

(1 - x)^{6} : 1 - 6 x + 15 x^{2} - 20 x^{3} + 15 x^{4} - 6 x^{5} + x^{6}

64 x^{6} + 960 x^{5} + 6000 x^{4} + 20000 x^{3} + 37500 x^{2} + 37500 x + 15625 = 1 - 6 x + 15 x^{2} - 20 x^{3} + 15 x^{4} - 6 x^{5} + x^{6}

Restar

1 - 6 x + 15 x^{2} - 20 x^{3} + 15 x^{4} - 6 x^{5} + x^{6}

de ambos lados

64 x^{6} + 960 x^{5} + 6000 x^{4} + 20000 x^{3} + 37500 x^{2} + 37500 x + 15625 - (1 - 6 x + 15 x^{2} - 20 x^{3} + 15 x^{4} - 6 x^{5} + x^{6}) = 1 - 6 x + 15 x^{2} - 20 x^{3} + 15 x^{4} - 6 x^{5} + x^{6} - (1 - 6 x + 15 x^{2} - 20 x^{3} + 15 x^{4} - 6 x^{5} + x^{6})

Simplificar

63 x^{6} + 966 x^{5} + 5985 x^{4} + 20020 x^{3} + 37485 x^{2} + 37506 x + 15624 = 0

Factorizar

63 x^{6} + 966 x^{5} + 5985 x^{4} + 20020 x^{3} + 37485 x^{2} + 37506 x + 15624 : 7 (x + 6) (3 x + 4) (3 x^{4} + 24 x^{3} + 85 x^{2} + 138 x + 93)

7 (x + 6) (3 x + 4) (3 x^{4} + 24 x^{3} + 85 x^{2} + 138 x + 93) = 0

Utilizando el teorema de factor cero: si

ab = 0

entonces

a = 0

o

b = 0

x + 6 = 0 or 3 x + 4 = 0 or 3 x^{4} + 24 x^{3} + 85 x^{2} + 138 x + 93 = 0

Resolver

x + 6 = 0 : x = - 6

Resolver

3 x + 4 = 0 : x = - \frac{4}{3}

Resolver

3 x^{4} + 24 x^{3} + 85 x^{2} + 138 x + 93 = 0 :

Sin solución para

x \in R

Las soluciones son

x = - 6, x = - \frac{4}{3}

Ejemplos populares

(3 x - 7)^{3} + 1 = 5

25x^2(x+3)-9(x+3)=0

25 x^{2} (x + 3) - 9 (x + 3) = 0

(x^2-x)^2-8(x^2-x)+12=0

(x^{2} - x)^{2} - 8 (x^{2} - x) + 12 = 0

y = (y^{2})^{2}

x (x + 2) (x + 4) = 4