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Popular Álgebra >

(x^{12}-1)8=x^{84}-1

Solución

(x^{12} - 1) 8 = x^{84} - 1

Solución

x = 1, x = - 1, x = 6 \frac{5.22107 E 13}{5.0 E 13}, x = - 6 \frac{5.22107 E 13}{5.0 E 13}

+1

Decimal

x = 1, x = - 1, x = 1.00361 \dots, x = - 1.00361 \dots

Pasos de solución

(x^{12} - 1) \cdot 8 = x^{84} - 1

Desarrollar

(x^{12} - 1) \cdot 8 : 8 x^{12} - 8

8 x^{12} - 8 = x^{84} - 1

Intercambiar lados

x^{84} - 1 = 8 x^{12} - 8

Desplace

8

a la izquierda

x^{84} + 7 = 8 x^{12}

Desplace

8 x^{12}

a la izquierda

x^{84} + 7 - 8 x^{12} = 0

Escribir en la forma binómica

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

x^{84} - 8 x^{12} + 7 = 0

Re-escribir la ecuación con

u = x^{2}, u^{6} = x^{12}

y

u^{42} = x^{84}

u^{42} - 8 u^{6} + 7 = 0

Resolver

u^{42} - 8 u^{6} + 7 = 0 : u = 1, u = - 1, u = 3 \frac{5.22107 E 13}{5.0 E 13}, u = - 3 \frac{5.22107 E 13}{5.0 E 13}

u = 1, u = - 1, u = 3 \frac{5.22107 E 13}{5.0 E 13}, u = - 3 \frac{5.22107 E 13}{5.0 E 13}

Sustituir hacia atrás la

u = x^{2},

resolver para

x

Resolver

x^{2} = 1 : x = 1, x = - 1

Resolver

x^{2} = - 1 :

Sin solución para

x \in R

Resolver

x^{2} = 3 \frac{5.22107 E 13}{5.0 E 13} : x = 6 \frac{5.22107 E 13}{5.0 E 13}, x = - 6 \frac{5.22107 E 13}{5.0 E 13}

Resolver

x^{2} = - 3 \frac{5.22107 E 13}{5.0 E 13} :

Sin solución para

x \in R

Las soluciones son

x = 1, x = - 1, x = 6 \frac{5.22107 E 13}{5.0 E 13}, x = - 6 \frac{5.22107 E 13}{5.0 E 13}

Gráfica

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