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Popular >

(x^4)^2=16-15(x^2)^2

Solución

(x^{4})^{2} = 16 - 15 (x^{2})^{2}

Solución

x = 1, x = - 1, x = i, x = - i, x = 2 + 2 i, x = - 2 - 2 i, x = 2 - 2 i, x = - 2 + 2 i

Pasos de solución

(x^{4})^{2} = 16 - 15 (x^{2})^{2}

Desarrollar

(x^{4})^{2} : x^{8}

Desarrollar

16 - 15 (x^{2})^{2} : 16 - 15 x^{4}

x^{8} = 16 - 15 x^{4}

Mover

15 x^{4}

al lado izquierdo

x^{8} + 15 x^{4} = 16

Mover

16

al lado izquierdo

x^{8} + 15 x^{4} - 16 = 0

Re-escribir la ecuación con

u = x^{2}, u^{2} = x^{4}

y

u^{4} = x^{8}

u^{4} + 15 u^{2} - 16 = 0

Resolver

u^{4} + 15 u^{2} - 16 = 0 : u = 1, u = - 1, u = 4 i, u = - 4 i

u = 1, u = - 1, u = 4 i, u = - 4 i

Sustituir hacia atrás la

u = x^{2},

resolver para

x

Resolver

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

Resolver

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

Resolver

x^{2} = 4 i : x = 2 + 2 i, x = - 2 - 2 i

Resolver

x^{2} = - 4 i : x = 2 - 2 i, x = - 2 + 2 i

Las soluciones son

x = 1, x = - 1, x = i, x = - i, x = 2 + 2 i, x = - 2 - 2 i, x = 2 - 2 i, x = - 2 + 2 i

Ejemplos populares

x^4-x^3-x^2-1=0

x^{4} - x^{3} - x^{2} - 1 = 0

-x^4+x^3+2x^2-1=0

- x^{4} + x^{3} + 2 x^{2} - 1 = 0

2x^3+0x^2+7x-8=0

2 x^{3} + 0 x^{2} + 7 x - 8 = 0

a^{4} - 10 a^{2} = - 21

a^{3} = - 8