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Beliebt Algebra >

x^4+x^2-1=0

Lösung

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

Lösung

x = \frac{- 1 + 5}{2}, x = - \frac{- 1 + 5}{2}, x = \frac{- 1 - 5}{2}, x = - \frac{- 1 - 5}{2}

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 + 5}{2}, u = \frac{- 1 - 5}{2}

u = \frac{- 1 + 5}{2}, u = \frac{- 1 - 5}{2}

Setze

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

löse für

x

Löse

x^{2} = \frac{- 1 + 5}{2} : x = \frac{- 1 + 5}{2}, x = - \frac{- 1 + 5}{2}

Löse

x^{2} = \frac{- 1 - 5}{2} : x = \frac{- 1 - 5}{2}, x = - \frac{- 1 - 5}{2}

Die Lösungen sind

x = \frac{- 1 + 5}{2}, x = - \frac{- 1 + 5}{2}, x = \frac{- 1 - 5}{2}, x = - \frac{- 1 - 5}{2}

Graph

Beliebte Beispiele

x^{4} = - 1

x^4-x^3-4x^2+4x=0

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

z^{4} + 13 z^{2} + 36 = 0

x^4+x^3-4x^2+x+1=0

x^{4} + x^{3} - 4 x^{2} + x + 1 = 0

x^{3} = 4