es

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Álgebra >

(2x-1)^6=(2x-1)^8

Solución

(2 x - 1)^{6} = (2 x - 1)^{8}

Solución

x = 0, x = 1, x = \frac{1}{2}

+1

Decimal

x = 0, x = 1, x = 0.5

Pasos de solución

(2 x - 1)^{6} = (2 x - 1)^{8}

Desarrollar

(2 x - 1)^{6} : 64 x^{6} - 192 x^{5} + 240 x^{4} - 160 x^{3} + 60 x^{2} - 12 x + 1

Desarrollar

(2 x - 1)^{8} : 256 x^{8} - 1024 x^{7} + 1792 x^{6} - 1792 x^{5} + 1120 x^{4} - 448 x^{3} + 112 x^{2} - 16 x + 1

64 x^{6} - 192 x^{5} + 240 x^{4} - 160 x^{3} + 60 x^{2} - 12 x + 1 = 256 x^{8} - 1024 x^{7} + 1792 x^{6} - 1792 x^{5} + 1120 x^{4} - 448 x^{3} + 112 x^{2} - 16 x + 1

Intercambiar lados

256 x^{8} - 1024 x^{7} + 1792 x^{6} - 1792 x^{5} + 1120 x^{4} - 448 x^{3} + 112 x^{2} - 16 x + 1 = 64 x^{6} - 192 x^{5} + 240 x^{4} - 160 x^{3} + 60 x^{2} - 12 x + 1

Desplace

1

a la derecha

256 x^{8} - 1024 x^{7} + 1792 x^{6} - 1792 x^{5} + 1120 x^{4} - 448 x^{3} + 112 x^{2} - 16 x = 64 x^{6} - 192 x^{5} + 240 x^{4} - 160 x^{3} + 60 x^{2} - 12 x

Restar

64 x^{6} - 192 x^{5} + 240 x^{4} - 160 x^{3} + 60 x^{2} - 12 x

de ambos lados

256 x^{8} - 1024 x^{7} + 1792 x^{6} - 1792 x^{5} + 1120 x^{4} - 448 x^{3} + 112 x^{2} - 16 x - (64 x^{6} - 192 x^{5} + 240 x^{4} - 160 x^{3} + 60 x^{2} - 12 x) = 64 x^{6} - 192 x^{5} + 240 x^{4} - 160 x^{3} + 60 x^{2} - 12 x - (64 x^{6} - 192 x^{5} + 240 x^{4} - 160 x^{3} + 60 x^{2} - 12 x)

Simplificar

256 x^{8} - 1024 x^{7} + 1728 x^{6} - 1600 x^{5} + 880 x^{4} - 288 x^{3} + 52 x^{2} - 4 x = 0

Factorizar

256 x^{8} - 1024 x^{7} + 1728 x^{6} - 1600 x^{5} + 880 x^{4} - 288 x^{3} + 52 x^{2} - 4 x : 4 x (x - 1) (2 x - 1)^{6}

4 x (x - 1) (2 x - 1)^{6} = 0

Usando la propiedad del factor cero:

Si

ab = 0

entonces

a = 0

o

b = 0

x = 0 or x - 1 = 0 or 2 x - 1 = 0

Resolver

x - 1 = 0 : x = 1

Resolver

2 x - 1 = 0 : x = \frac{1}{2}

Las soluciones son

x = 0, x = 1, x = \frac{1}{2}

Gráfica

Ejemplos populares

C^8=(ln(7)+C)/7

-x^3+3x^2+62x-184=0

x^3-2x^2+8-4x=0