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Beliebt Algebra >

16x^8-4x^4-56=0

Lösung

16 x^{8} - 4 x^{4} - 56 = 0

Lösung

x = 2, x = - 2, x = 2 i, x = - 2 i, x = \frac{4 7}{2} + \frac{4 7}{2} i, x = - \frac{4 7}{2} - \frac{4 7}{2} i, x = \frac{4 7}{2} - \frac{4 7}{2} i, x = - \frac{4 7}{2} + \frac{4 7}{2} i

Schritte zur Lösung

16 x^{8} - 4 x^{4} - 56 = 0

Schreibe die Gleichung um mit

u = x^{2}, u^{2} = x^{4}

und

u^{4} = x^{8}

16 u^{4} - 4 u^{2} - 56 = 0

Löse

16 u^{4} - 4 u^{2} - 56 = 0 : u = 2, u = - 2, u = \frac{7}{2} i, u = - \frac{7}{2} i

u = 2, u = - 2, u = \frac{7}{2} i, u = - \frac{7}{2} i

Setze

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

löse für

x

Löse

x^{2} = 2 : x = 2, x = - 2

Löse

x^{2} = - 2 : x = 2 i, x = - 2 i

Löse

x^{2} = \frac{7}{2} i : x = \frac{4 7}{2} + \frac{4 7}{2} i, x = - \frac{4 7}{2} - \frac{4 7}{2} i

Löse

x^{2} = - \frac{7}{2} i : x = \frac{4 7}{2} - \frac{4 7}{2} i, x = - \frac{4 7}{2} + \frac{4 7}{2} i

Die Lösungen sind

x = 2, x = - 2, x = 2 i, x = - 2 i, x = \frac{4 7}{2} + \frac{4 7}{2} i, x = - \frac{4 7}{2} - \frac{4 7}{2} i, x = \frac{4 7}{2} - \frac{4 7}{2} i, x = - \frac{4 7}{2} + \frac{4 7}{2} i

Graph

Beliebte Beispiele

x^{8} + 80 x^{4} = 81

16 y^{3} - 25 y = 0

x^{3} \cdot (2 x - 6) = 0

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

x^{4} - 25 = 0