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Beliebt Algebra >

x^4+x^2+17=0

Lösung

x^{4} + x^{2} + 17 = 0

Lösung

x = \frac{- 1 + 2 17}{2} + \frac{67}{2 - 1 + 2 17} i, x = - \frac{- 1 + 2 17}{2} - \frac{67}{2 - 1 + 2 17} i, x = \frac{- 1 + 2 17}{2} - \frac{67}{2 - 1 + 2 17} i, x = - \frac{- 1 + 2 17}{2} + \frac{67}{2 - 1 + 2 17} i

Schritte zur Lösung

x^{4} + x^{2} + 17 = 0

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

u^{2} + u + 17 = 0

Löse

u^{2} + u + 17 = 0 : u = - \frac{1}{2} + i \frac{67}{2}, u = - \frac{1}{2} - i \frac{67}{2}

u = - \frac{1}{2} + i \frac{67}{2}, u = - \frac{1}{2} - i \frac{67}{2}

Setze

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

löse für

x

Löse

x^{2} = - \frac{1}{2} + i \frac{67}{2} : x = \frac{- 1 + 2 17}{2} + \frac{67}{2 - 1 + 2 17} i, x = - \frac{- 1 + 2 17}{2} - \frac{67}{2 - 1 + 2 17} i

Löse

x^{2} = - \frac{1}{2} - i \frac{67}{2} : x = \frac{- 1 + 2 17}{2} - \frac{67}{2 - 1 + 2 17} i, x = - \frac{- 1 + 2 17}{2} + \frac{67}{2 - 1 + 2 17} i

Die Lösungen sind

x = \frac{- 1 + 2 17}{2} + \frac{67}{2 - 1 + 2 17} i, x = - \frac{- 1 + 2 17}{2} - \frac{67}{2 - 1 + 2 17} i, x = \frac{- 1 + 2 17}{2} - \frac{67}{2 - 1 + 2 17} i, x = - \frac{- 1 + 2 17}{2} + \frac{67}{2 - 1 + 2 17} i

Graph

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