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Beliebt Algebra >

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

Lösung

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

Lösung

x = \frac{1 + 4 2}{2 2} + \frac{31}{2 2 1 + 4 2} i, x = - \frac{1 + 4 2}{2 2} - \frac{31}{2 2 1 + 4 2} i, x = \frac{1 + 4 2}{2 2} - \frac{31}{2 2 1 + 4 2} i, x = - \frac{1 + 4 2}{2 2} + \frac{31}{2 2 1 + 4 2} i

Schritte zur Lösung

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

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

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

Löse

2 u^{2} - u + 4 = 0 : u = \frac{1}{4} + i \frac{31}{4}, u = \frac{1}{4} - i \frac{31}{4}

u = \frac{1}{4} + i \frac{31}{4}, u = \frac{1}{4} - i \frac{31}{4}

Setze

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

löse für

x

Löse

x^{2} = \frac{1}{4} + i \frac{31}{4} : x = \frac{1 + 4 2}{2 2} + \frac{31}{2 2 1 + 4 2} i, x = - \frac{1 + 4 2}{2 2} - \frac{31}{2 2 1 + 4 2} i

Löse

x^{2} = \frac{1}{4} - i \frac{31}{4} : x = \frac{1 + 4 2}{2 2} - \frac{31}{2 2 1 + 4 2} i, x = - \frac{1 + 4 2}{2 2} + \frac{31}{2 2 1 + 4 2} i

Die Lösungen sind

x = \frac{1 + 4 2}{2 2} + \frac{31}{2 2 1 + 4 2} i, x = - \frac{1 + 4 2}{2 2} - \frac{31}{2 2 1 + 4 2} i, x = \frac{1 + 4 2}{2 2} - \frac{31}{2 2 1 + 4 2} i, x = - \frac{1 + 4 2}{2 2} + \frac{31}{2 2 1 + 4 2} i

Graph

Beliebte Beispiele

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