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Beliebt Algebra >

(-2x^4+3x^2-5)=(x-x)

Lösung

(- 2 x^{4} + 3 x^{2} - 5) = (x - x)

Lösung

x = \frac{3 + 2 10}{2 2} - \frac{31}{2 2 3 + 2 10} i, x = - \frac{3 + 2 10}{2 2} + \frac{31}{2 2 3 + 2 10} i, x = \frac{3 + 2 10}{2 2} + \frac{31}{2 2 3 + 2 10} i, x = - \frac{3 + 2 10}{2 2} - \frac{31}{2 2 3 + 2 10} i

Schritte zur Lösung

(- 2 x^{4} + 3 x^{2} - 5) = (x - x)

Fasse zusammen

- 2 x^{4} + 3 x^{2} - 5 = 0

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

- 2 u^{2} + 3 u - 5 = 0

Löse

- 2 u^{2} + 3 u - 5 = 0 : u = \frac{3}{4} - i \frac{31}{4}, u = \frac{3}{4} + i \frac{31}{4}

u = \frac{3}{4} - i \frac{31}{4}, u = \frac{3}{4} + i \frac{31}{4}

Setze

u = x^{2} w i e d er e in,

löse für

x

Löse

x^{2} = \frac{3}{4} - i \frac{31}{4} : x = \frac{3 + 2 10}{2 2} - \frac{31}{2 2 3 + 2 10} i, x = - \frac{3 + 2 10}{2 2} + \frac{31}{2 2 3 + 2 10} i

Löse

x^{2} = \frac{3}{4} + i \frac{31}{4} : x = \frac{3 + 2 10}{2 2} + \frac{31}{2 2 3 + 2 10} i, x = - \frac{3 + 2 10}{2 2} - \frac{31}{2 2 3 + 2 10} i

Die Lösungen sind

x = \frac{3 + 2 10}{2 2} - \frac{31}{2 2 3 + 2 10} i, x = - \frac{3 + 2 10}{2 2} + \frac{31}{2 2 3 + 2 10} i, x = \frac{3 + 2 10}{2 2} + \frac{31}{2 2 3 + 2 10} i, x = - \frac{3 + 2 10}{2 2} - \frac{31}{2 2 3 + 2 10} i

Graph

Beliebte Beispiele

x^{5} + x - 2 = 0

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e a^{4} = 5, a^{1} = 20

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

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