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Popular Álgebra >

2+6-1=x^{16}-4

Solución

2 + 6 - 1 = x^{16} - 4

Solución

x = 811, x = - 811, x = 811 i, x = - 811 i, x = \frac{16 11}{2} + \frac{4 4 11}{2} i, x = - \frac{16 11}{2} - \frac{4 4 11}{2} i, x = - \frac{16 11}{2} + \frac{4 4 11}{2} i, x = \frac{16 11}{2} - \frac{4 4 11}{2} i, x = \frac{16 11}{2 2 - 2} + \frac{8 11 ( 2 - 2 )}{2} i, x = - \frac{16 11}{2 2 - 2} - \frac{8 11 ( 2 - 2 )}{2} i, x = - \frac{16 11}{2 2 + 2} + \frac{8 11 ( 2 + 2 )}{2} i, x = \frac{16 11}{2 2 + 2} - \frac{8 11 ( 2 + 2 )}{2} i, x = \frac{16 11}{2 2 + 2} + \frac{8 11 ( 2 + 2 )}{2} i, x = - \frac{16 11}{2 2 + 2} - \frac{8 11 ( 2 + 2 )}{2} i, x = - \frac{16 11}{2 2 - 2} + \frac{8 11 ( 2 - 2 )}{2} i, x = \frac{16 11}{2 2 - 2} - \frac{8 11 ( 2 - 2 )}{2} i

Pasos de solución

2 + 6 - 1 = x^{16} - 4

Intercambiar lados

x^{16} - 4 = 2 + 6 - 1

Desplace

4

a la derecha

x^{16} = 11

Re-escribir la ecuación con

u = x^{2}

y

u^{8} = x^{16}

u^{8} = 11

Resolver

u^{8} = 11 : u = 411, u = - 411, u = 411 i, u = - 411 i, u = \frac{8 11}{2} + \frac{4 11}{2} i, u = - \frac{8 11}{2} - \frac{4 11}{2} i, u = - \frac{8 11}{2} + \frac{4 11}{2} i, u = \frac{8 11}{2} - \frac{4 11}{2} i

u = 411, u = - 411, u = 411 i, u = - 411 i, u = \frac{8 11}{2} + \frac{4 11}{2} i, u = - \frac{8 11}{2} - \frac{4 11}{2} i, u = - \frac{8 11}{2} + \frac{4 11}{2} i, u = \frac{8 11}{2} - \frac{4 11}{2} i

Sustituir hacia atrás la

u = x^{2},

resolver para

x

Resolver

x^{2} = 411 : x = 811, x = - 811

Resolver

x^{2} = - 411 : x = 811 i, x = - 811 i

Resolver

x^{2} = 411 i : x = \frac{16 11}{2} + \frac{4 4 11}{2} i, x = - \frac{16 11}{2} - \frac{4 4 11}{2} i

Resolver

x^{2} = - 411 i : x = - \frac{16 11}{2} + \frac{4 4 11}{2} i, x = \frac{16 11}{2} - \frac{4 4 11}{2} i

Resolver

x^{2} = \frac{8 11}{2} + \frac{4 11}{2} i : x = \frac{16 11}{2 2 - 2} + \frac{8 11 ( 2 - 2 )}{2} i, x = - \frac{16 11}{2 2 - 2} - \frac{8 11 ( 2 - 2 )}{2} i

Resolver

x^{2} = - \frac{8 11}{2} - \frac{4 11}{2} i : x = - \frac{16 11}{2 2 + 2} + \frac{8 11 ( 2 + 2 )}{2} i, x = \frac{16 11}{2 2 + 2} - \frac{8 11 ( 2 + 2 )}{2} i

Resolver

x^{2} = - \frac{8 11}{2} + \frac{4 11}{2} i : x = \frac{16 11}{2 2 + 2} + \frac{8 11 ( 2 + 2 )}{2} i, x = - \frac{16 11}{2 2 + 2} - \frac{8 11 ( 2 + 2 )}{2} i

Resolver

x^{2} = \frac{8 11}{2} - \frac{4 11}{2} i : x = - \frac{16 11}{2 2 - 2} + \frac{8 11 ( 2 - 2 )}{2} i, x = \frac{16 11}{2 2 - 2} - \frac{8 11 ( 2 - 2 )}{2} i

Las soluciones son

x = 811, x = - 811, x = 811 i, x = - 811 i, x = \frac{16 11}{2} + \frac{4 4 11}{2} i, x = - \frac{16 11}{2} - \frac{4 4 11}{2} i, x = - \frac{16 11}{2} + \frac{4 4 11}{2} i, x = \frac{16 11}{2} - \frac{4 4 11}{2} i, x = \frac{16 11}{2 2 - 2} + \frac{8 11 ( 2 - 2 )}{2} i, x = - \frac{16 11}{2 2 - 2} - \frac{8 11 ( 2 - 2 )}{2} i, x = - \frac{16 11}{2 2 + 2} + \frac{8 11 ( 2 + 2 )}{2} i, x = \frac{16 11}{2 2 + 2} - \frac{8 11 ( 2 + 2 )}{2} i, x = \frac{16 11}{2 2 + 2} + \frac{8 11 ( 2 + 2 )}{2} i, x = - \frac{16 11}{2 2 + 2} - \frac{8 11 ( 2 + 2 )}{2} i, x = - \frac{16 11}{2 2 - 2} + \frac{8 11 ( 2 - 2 )}{2} i, x = \frac{16 11}{2 2 - 2} - \frac{8 11 ( 2 - 2 )}{2} i

Gráfica

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