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Beliebt Algebra >

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

Lösung

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

Lösung

x = \frac{- 3 + 13}{2}, x = - \frac{- 3 + 13}{2}, x = \frac{- 3 - 13}{2}, x = - \frac{- 3 - 13}{2}

Schritte zur Lösung

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

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

u^{2} + 3 u - 1 = 0

Löse

u^{2} + 3 u - 1 = 0 : u = \frac{- 3 + 13}{2}, u = \frac{- 3 - 13}{2}

u = \frac{- 3 + 13}{2}, u = \frac{- 3 - 13}{2}

Setze

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

löse für

x

Löse

x^{2} = \frac{- 3 + 13}{2} : x = \frac{- 3 + 13}{2}, x = - \frac{- 3 + 13}{2}

Löse

x^{2} = \frac{- 3 - 13}{2} : x = \frac{- 3 - 13}{2}, x = - \frac{- 3 - 13}{2}

Die Lösungen sind

x = \frac{- 3 + 13}{2}, x = - \frac{- 3 + 13}{2}, x = \frac{- 3 - 13}{2}, x = - \frac{- 3 - 13}{2}

Graph

Beliebte Beispiele

n^2=(n(n+1)(2n+1))/6

n^{2} = \frac{n ( n + 1 ) ( 2 n + 1 )}{6}

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

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

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

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