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Popular Álgebra >

2(2x^4-3x^2)+2=-2x^2(x^2+2)+x^2+11

Solución

2 (2 x^{4} - 3 x^{2}) + 2 = - 2 x^{2} (x^{2} + 2) + x^{2} + 11

Solución

x = \frac{3}{2}, x = - \frac{3}{2}, x = i, x = - i

Pasos de solución

2 (2 x^{4} - 3 x^{2}) + 2 = - 2 x^{2} (x^{2} + 2) + x^{2} + 11

Desarrollar

2 (2 x^{4} - 3 x^{2}) + 2 : 4 x^{4} - 6 x^{2} + 2

Desarrollar

- 2 x^{2} (x^{2} + 2) + x^{2} + 11 : - 2 x^{4} - 3 x^{2} + 11

4 x^{4} - 6 x^{2} + 2 = - 2 x^{4} - 3 x^{2} + 11

Desplace

11

a la izquierda

4 x^{4} - 6 x^{2} - 9 = - 2 x^{4} - 3 x^{2}

Desplace

3 x^{2}

a la izquierda

4 x^{4} - 3 x^{2} - 9 = - 2 x^{4}

Desplace

2 x^{4}

a la izquierda

6 x^{4} - 3 x^{2} - 9 = 0

Re-escribir la ecuación con

u = x^{2}

y

u^{2} = x^{4}

6 u^{2} - 3 u - 9 = 0

Resolver

6 u^{2} - 3 u - 9 = 0 : u = \frac{3}{2}, u = - 1

u = \frac{3}{2}, u = - 1

Sustituir hacia atrás la

u = x^{2},

resolver para

x

Resolver

x^{2} = \frac{3}{2} : x = \frac{3}{2}, x = - \frac{3}{2}

Resolver

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

Las soluciones son

x = \frac{3}{2}, x = - \frac{3}{2}, x = i, x = - i

Gráfica

Ejemplos populares

a^{3} = 64

x^3+2020x^2+20x-5=0

x^{3} + 2020 x^{2} + 20 x - 5 = 0

x^{4} = - 16 x^{2}

a^4=49+20sqrt(6)

a^{4} = 49 + 206

2 x^{6} - 17 x^{3} + 8 = 0