16x^4-4x^2+1=0

Solución

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

x = \frac{3}{4} + \frac{1}{4} i, x = - \frac{3}{4} - \frac{1}{4} i, x = \frac{3}{4} - \frac{1}{4} i, x = - \frac{3}{4} + \frac{1}{4} i

Pasos de solución

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

Re-escribir la ecuación con

u = x^{2}

u^{2} = x^{4}

16 u^{2} - 4 u + 1 = 0

Resolver

16 u^{2} - 4 u + 1 = 0 : u = \frac{1}{8} + i \frac{3}{8}, u = \frac{1}{8} - i \frac{3}{8}

u = \frac{1}{8} + i \frac{3}{8}, u = \frac{1}{8} - i \frac{3}{8}

Sustituir hacia atrás la

u = x^{2},

resolver para

x

Resolver

x^{2} = \frac{1}{8} + i \frac{3}{8} : x = \frac{3}{4} + \frac{1}{4} i, x = - \frac{3}{4} - \frac{1}{4} i

Resolver

x^{2} = \frac{1}{8} - i \frac{3}{8} : x = \frac{3}{4} - \frac{1}{4} i, x = - \frac{3}{4} + \frac{1}{4} i

Las soluciones son

x = \frac{3}{4} + \frac{1}{4} i, x = - \frac{3}{4} - \frac{1}{4} i, x = \frac{3}{4} - \frac{1}{4} i, x = - \frac{3}{4} + \frac{1}{4} i

x^{10} + 5 x^{5} + 6 = 0

y, x = y^{11}

0 = 36 x - x^{3}

z (z^{2} + 1) = 0

6 c^{5} + 4 c^{3} = 2