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Popular Álgebra >

x^2(x^2+4)(x^2+16)=100

Solución

x^{2} (x^{2} + 4) (x^{2} + 16) = 100

Solución

x = \frac{2.84044 E 15}{2.5 E 15}, x = - \frac{2.84044 E 15}{2.5 E 15}

+1

Decimal

x = 1.06591 \dots, x = - 1.06591 \dots

Pasos de solución

x^{2} (x^{2} + 4) (x^{2} + 16) = 100

Desarrollar

x^{2} (x^{2} + 4) (x^{2} + 16) : x^{6} + 20 x^{4} + 64 x^{2}

x^{6} + 20 x^{4} + 64 x^{2} = 100

Desplace

100

a la izquierda

x^{6} + 20 x^{4} + 64 x^{2} - 100 = 0

Re-escribir la ecuación con

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

y

u^{3} = x^{6}

u^{3} + 20 u^{2} + 64 u - 100 = 0

Resolver

u^{3} + 20 u^{2} + 64 u - 100 = 0 : u \approx 1.13617 \dots, u \approx - 5.70290 \dots, u \approx - 15.43327 \dots

u \approx 1.13617 \dots, u \approx - 5.70290 \dots, u \approx - 15.43327 \dots

Sustituir hacia atrás la

u = x^{2},

resolver para

x

Resolver

x^{2} = 1.13617 \dots : x = \frac{2.84044 E 15}{2.5 E 15}, x = - \frac{2.84044 E 15}{2.5 E 15}

Resolver

x^{2} = - 5.70290 \dots :

Sin solución para

x \in R

Resolver

x^{2} = - 15.43327 \dots :

Sin solución para

x \in R

Las soluciones son

x = \frac{2.84044 E 15}{2.5 E 15}, x = - \frac{2.84044 E 15}{2.5 E 15}

Gráfica

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