x^4-6/7 x^2+3/35 =0

Solución

x^{4} - \frac{6}{7} x^{2} + \frac{3}{35} = 0

x = \frac{15 + 2 30}{35}, x = - \frac{15 + 2 30}{35}, x = \frac{15 - 2 30}{35}, x = - \frac{15 - 2 30}{35}

Notación decimal

x = 0.86113 \dots, x = - 0.86113 \dots, x = 0.33998 \dots, x = - 0.33998 \dots

Pasos de solución

x^{4} - \frac{6}{7} x^{2} + \frac{3}{35} = 0

Encontrar el mínimo común múltiplo de

7, 35 : 35

Multiplicar por el mínimo común múltiplo=

35

x^{4} \cdot 35 - \frac{6}{7} x^{2} \cdot 35 + \frac{3}{35} \cdot 35 = 0 \cdot 35

Simplificar

35 x^{4} - 30 x^{2} + 3 = 0

Re-escribir la ecuación con

u = x^{2}

u^{2} = x^{4}

35 u^{2} - 30 u + 3 = 0

Resolver

35 u^{2} - 30 u + 3 = 0 : u = \frac{15 + 2 30}{35}, u = \frac{15 - 2 30}{35}

u = \frac{15 + 2 30}{35}, u = \frac{15 - 2 30}{35}

Sustituir hacia atrás la

u = x^{2},

resolver para

x

Resolver

x^{2} = \frac{15 + 2 30}{35} : x = \frac{15 + 2 30}{35}, x = - \frac{15 + 2 30}{35}

Resolver

x^{2} = \frac{15 - 2 30}{35} : x = \frac{15 - 2 30}{35}, x = - \frac{15 - 2 30}{35}

Las soluciones son

x = \frac{15 + 2 30}{35}, x = - \frac{15 + 2 30}{35}, x = \frac{15 - 2 30}{35}, x = - \frac{15 - 2 30}{35}

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

5 x^{4} + 7 x^{2} - 12 = 0

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

x^{16} + 5 x^{8} + 4 = 0

x^{3} + 4 x^{2} + x - 6