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Beliebt Algebra >

1+x^2+x^4=0

Lösung

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

Lösung

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

Schritte zur Lösung

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

Schreibe in der Standard Form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

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

Löse

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

Die Lösungen sind

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

Graph

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