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Beliebt Algebra >

x^4-x^2+1=0

Lösung

x^{4} - x^{2} + 1 = 0

Lösung

x = \frac{3}{2} + \frac{1}{2} i, x = - \frac{3}{2} - \frac{1}{2} i, x = \frac{3}{2} - \frac{1}{2} i, x = - \frac{3}{2} + \frac{1}{2} i

Schritte zur Lösung

x^{4} - x^{2} + 1 = 0

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

u^{2} - u + 1 = 0

Löse

u^{2} - u + 1 = 0 : u = \frac{1}{2} + i \frac{3}{2}, u = \frac{1}{2} - i \frac{3}{2}

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

Setze

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

löse für

x

Löse

x^{2} = \frac{1}{2} + i \frac{3}{2} : x = \frac{3}{2} + \frac{1}{2} i, x = - \frac{3}{2} - \frac{1}{2} i

Löse

x^{2} = \frac{1}{2} - i \frac{3}{2} : x = \frac{3}{2} - \frac{1}{2} i, x = - \frac{3}{2} + \frac{1}{2} i

Die Lösungen sind

x = \frac{3}{2} + \frac{1}{2} i, x = - \frac{3}{2} - \frac{1}{2} i, x = \frac{3}{2} - \frac{1}{2} i, x = - \frac{3}{2} + \frac{1}{2} i

Graph

Beliebte Beispiele

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

8 x^{4} = x

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x^{3} - 5 x^{2} + 6 x = 0

(x^{2} + 1)^{3} = 0