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Beliebt Algebra >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

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

Löse

u^{2} + 2 u + 3 = 0 : u = - 1 + 2 i, u = - 1 - 2 i

u = - 1 + 2 i, u = - 1 - 2 i

Setze

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

löse für

x

Löse

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

Löse

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

Die Lösungen sind

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

Graph

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