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Beliebt Algebra >

2+6-1=x^{16}-4

Lösung

2 + 6 - 1 = x^{16} - 4

Lösung

x = 811, x = - 811, x = 811 i, x = - 811 i, x = \frac{16 11}{2} + \frac{4 4 11}{2} i, x = - \frac{16 11}{2} - \frac{4 4 11}{2} i, x = - \frac{16 11}{2} + \frac{4 4 11}{2} i, x = \frac{16 11}{2} - \frac{4 4 11}{2} i, x = \frac{16 11}{2 2 - 2} + \frac{8 11 ( 2 - 2 )}{2} i, x = - \frac{16 11}{2 2 - 2} - \frac{8 11 ( 2 - 2 )}{2} i, x = - \frac{16 11}{2 2 + 2} + \frac{8 11 ( 2 + 2 )}{2} i, x = \frac{16 11}{2 2 + 2} - \frac{8 11 ( 2 + 2 )}{2} i, x = \frac{16 11}{2 2 + 2} + \frac{8 11 ( 2 + 2 )}{2} i, x = - \frac{16 11}{2 2 + 2} - \frac{8 11 ( 2 + 2 )}{2} i, x = - \frac{16 11}{2 2 - 2} + \frac{8 11 ( 2 - 2 )}{2} i, x = \frac{16 11}{2 2 - 2} - \frac{8 11 ( 2 - 2 )}{2} i

Schritte zur Lösung

2 + 6 - 1 = x^{16} - 4

Tausche die Seiten

x^{16} - 4 = 2 + 6 - 1

Verschiebe

4

auf die rechte Seite

x^{16} = 11

Schreibe die Gleichung um mit

u = x^{2}

und

u^{8} = x^{16}

u^{8} = 11

Löse

u^{8} = 11 : u = 411, u = - 411, u = 411 i, u = - 411 i, u = \frac{8 11}{2} + \frac{4 11}{2} i, u = - \frac{8 11}{2} - \frac{4 11}{2} i, u = - \frac{8 11}{2} + \frac{4 11}{2} i, u = \frac{8 11}{2} - \frac{4 11}{2} i

u = 411, u = - 411, u = 411 i, u = - 411 i, u = \frac{8 11}{2} + \frac{4 11}{2} i, u = - \frac{8 11}{2} - \frac{4 11}{2} i, u = - \frac{8 11}{2} + \frac{4 11}{2} i, u = \frac{8 11}{2} - \frac{4 11}{2} i

Setze

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

löse für

x

Löse

x^{2} = 411 : x = 811, x = - 811

Löse

x^{2} = - 411 : x = 811 i, x = - 811 i

Löse

x^{2} = 411 i : x = \frac{16 11}{2} + \frac{4 4 11}{2} i, x = - \frac{16 11}{2} - \frac{4 4 11}{2} i

Löse

x^{2} = - 411 i : x = - \frac{16 11}{2} + \frac{4 4 11}{2} i, x = \frac{16 11}{2} - \frac{4 4 11}{2} i

Löse

x^{2} = \frac{8 11}{2} + \frac{4 11}{2} i : x = \frac{16 11}{2 2 - 2} + \frac{8 11 ( 2 - 2 )}{2} i, x = - \frac{16 11}{2 2 - 2} - \frac{8 11 ( 2 - 2 )}{2} i

Löse

x^{2} = - \frac{8 11}{2} - \frac{4 11}{2} i : x = - \frac{16 11}{2 2 + 2} + \frac{8 11 ( 2 + 2 )}{2} i, x = \frac{16 11}{2 2 + 2} - \frac{8 11 ( 2 + 2 )}{2} i

Löse

x^{2} = - \frac{8 11}{2} + \frac{4 11}{2} i : x = \frac{16 11}{2 2 + 2} + \frac{8 11 ( 2 + 2 )}{2} i, x = - \frac{16 11}{2 2 + 2} - \frac{8 11 ( 2 + 2 )}{2} i

Löse

x^{2} = \frac{8 11}{2} - \frac{4 11}{2} i : x = - \frac{16 11}{2 2 - 2} + \frac{8 11 ( 2 - 2 )}{2} i, x = \frac{16 11}{2 2 - 2} - \frac{8 11 ( 2 - 2 )}{2} i

Die Lösungen sind

x = 811, x = - 811, x = 811 i, x = - 811 i, x = \frac{16 11}{2} + \frac{4 4 11}{2} i, x = - \frac{16 11}{2} - \frac{4 4 11}{2} i, x = - \frac{16 11}{2} + \frac{4 4 11}{2} i, x = \frac{16 11}{2} - \frac{4 4 11}{2} i, x = \frac{16 11}{2 2 - 2} + \frac{8 11 ( 2 - 2 )}{2} i, x = - \frac{16 11}{2 2 - 2} - \frac{8 11 ( 2 - 2 )}{2} i, x = - \frac{16 11}{2 2 + 2} + \frac{8 11 ( 2 + 2 )}{2} i, x = \frac{16 11}{2 2 + 2} - \frac{8 11 ( 2 + 2 )}{2} i, x = \frac{16 11}{2 2 + 2} + \frac{8 11 ( 2 + 2 )}{2} i, x = - \frac{16 11}{2 2 + 2} - \frac{8 11 ( 2 + 2 )}{2} i, x = - \frac{16 11}{2 2 - 2} + \frac{8 11 ( 2 - 2 )}{2} i, x = \frac{16 11}{2 2 - 2} - \frac{8 11 ( 2 - 2 )}{2} i

Graph

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