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Beliebt Algebra >

x^4-16x^2+225=0

Lösung

x^{4} - 16 x^{2} + 225 = 0

Lösung

x = \frac{23}{2} + \frac{7}{2} i, x = - \frac{23}{2} - \frac{7}{2} i, x = \frac{23}{2} - \frac{7}{2} i, x = - \frac{23}{2} + \frac{7}{2} i

Schritte zur Lösung

x^{4} - 16 x^{2} + 225 = 0

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

u^{2} - 16 u + 225 = 0

Löse

u^{2} - 16 u + 225 = 0 : u = 8 + 161 i, u = 8 - 161 i

u = 8 + 161 i, u = 8 - 161 i

Setze

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

löse für

x

Löse

x^{2} = 8 + 161 i : x = \frac{23}{2} + \frac{7}{2} i, x = - \frac{23}{2} - \frac{7}{2} i

Löse

x^{2} = 8 - 161 i : x = \frac{23}{2} - \frac{7}{2} i, x = - \frac{23}{2} + \frac{7}{2} i

Die Lösungen sind

x = \frac{23}{2} + \frac{7}{2} i, x = - \frac{23}{2} - \frac{7}{2} i, x = \frac{23}{2} - \frac{7}{2} i, x = - \frac{23}{2} + \frac{7}{2} i

Graph

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