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Beliebt Algebra >

x^4-x^2+6=0

Lösung

x^{4} - x^{2} + 6 = 0

Lösung

x = \frac{1 + 2 6}{2} + \frac{23}{2 1 + 2 6} i, x = - \frac{1 + 2 6}{2} - \frac{23}{2 1 + 2 6} i, x = \frac{1 + 2 6}{2} - \frac{23}{2 1 + 2 6} i, x = - \frac{1 + 2 6}{2} + \frac{23}{2 1 + 2 6} i

Schritte zur Lösung

x^{4} - x^{2} + 6 = 0

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

u^{2} - u + 6 = 0

Löse

u^{2} - u + 6 = 0 : u = \frac{1}{2} + i \frac{23}{2}, u = \frac{1}{2} - i \frac{23}{2}

u = \frac{1}{2} + i \frac{23}{2}, u = \frac{1}{2} - i \frac{23}{2}

Setze

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

löse für

x

Löse

x^{2} = \frac{1}{2} + i \frac{23}{2} : x = \frac{1 + 2 6}{2} + \frac{23}{2 1 + 2 6} i, x = - \frac{1 + 2 6}{2} - \frac{23}{2 1 + 2 6} i

Löse

x^{2} = \frac{1}{2} - i \frac{23}{2} : x = \frac{1 + 2 6}{2} - \frac{23}{2 1 + 2 6} i, x = - \frac{1 + 2 6}{2} + \frac{23}{2 1 + 2 6} i

Die Lösungen sind

x = \frac{1 + 2 6}{2} + \frac{23}{2 1 + 2 6} i, x = - \frac{1 + 2 6}{2} - \frac{23}{2 1 + 2 6} i, x = \frac{1 + 2 6}{2} - \frac{23}{2 1 + 2 6} i, x = - \frac{1 + 2 6}{2} + \frac{23}{2 1 + 2 6} i

Graph

Beliebte Beispiele

6 x^{5} - 6 x = 0

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x^{3} + x^{2} - 14 x - 24 = 0

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x^4+8x^3-3x^2-26x-16=0

x^{4} + 8 x^{3} - 3 x^{2} - 26 x - 16 = 0

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