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Beliebt Algebra >

x^4-4x^2+7=0

Lösung

x^{4} - 4 x^{2} + 7 = 0

Lösung

x = \frac{2 + 7}{2} + \frac{3}{2 2 + 7} i, x = - \frac{2 + 7}{2} - \frac{3}{2 2 + 7} i, x = \frac{2 + 7}{2} - \frac{3}{2 2 + 7} i, x = - \frac{2 + 7}{2} + \frac{3}{2 2 + 7} i

Schritte zur Lösung

x^{4} - 4 x^{2} + 7 = 0

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

u^{2} - 4 u + 7 = 0

Löse

u^{2} - 4 u + 7 = 0 : u = 2 + 3 i, u = 2 - 3 i

u = 2 + 3 i, u = 2 - 3 i

Setze

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

löse für

x

Löse

x^{2} = 2 + 3 i : x = \frac{2 + 7}{2} + \frac{3}{2 2 + 7} i, x = - \frac{2 + 7}{2} - \frac{3}{2 2 + 7} i

Löse

x^{2} = 2 - 3 i : x = \frac{2 + 7}{2} - \frac{3}{2 2 + 7} i, x = - \frac{2 + 7}{2} + \frac{3}{2 2 + 7} i

Die Lösungen sind

x = \frac{2 + 7}{2} + \frac{3}{2 2 + 7} i, x = - \frac{2 + 7}{2} - \frac{3}{2 2 + 7} i, x = \frac{2 + 7}{2} - \frac{3}{2 2 + 7} i, x = - \frac{2 + 7}{2} + \frac{3}{2 2 + 7} i

Graph

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