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Beliebt Algebra >

x^6-2x^3+4=16

Lösung

x^{6} - 2 x^{3} + 4 = 16

Lösung

x = 3 1 + 13, x = - 3 1 + 13 \frac{1}{2} + 3 1 + 13 \frac{3}{2} i, x = - 3 1 + 13 \frac{1}{2} - 3 1 + 13 \frac{3}{2} i, x = 3 1 - 13, x = - 3 1 - 13 \frac{1}{2} + 3 1 - 13 \frac{3}{2} i, x = - 3 1 - 13 \frac{1}{2} - 3 1 - 13 \frac{3}{2} i

Schritte zur Lösung

x^{6} - 2 x^{3} + 4 = 16

Verschiebe

16

auf die linke Seite

x^{6} - 2 x^{3} - 12 = 0

Schreibe die Gleichung um mit

u = x^{3}

und

u^{2} = x^{6}

u^{2} - 2 u - 12 = 0

Löse

u^{2} - 2 u - 12 = 0 : u = 1 + 13, u = 1 - 13

u = 1 + 13, u = 1 - 13

Setze

u = x^{3} w i e d er e in,

löse für

x

Löse

x^{3} = 1 + 13 : x = 3 1 + 13, x = - 3 1 + 13 \frac{1}{2} + 3 1 + 13 \frac{3}{2} i, x = - 3 1 + 13 \frac{1}{2} - 3 1 + 13 \frac{3}{2} i

Löse

x^{3} = 1 - 13 : x = 3 1 - 13, x = - 3 1 - 13 \frac{1}{2} + 3 1 - 13 \frac{3}{2} i, x = - 3 1 - 13 \frac{1}{2} - 3 1 - 13 \frac{3}{2} i

Die Lösungen sind

x = 3 1 + 13, x = - 3 1 + 13 \frac{1}{2} + 3 1 + 13 \frac{3}{2} i, x = - 3 1 + 13 \frac{1}{2} - 3 1 + 13 \frac{3}{2} i, x = 3 1 - 13, x = - 3 1 - 13 \frac{1}{2} + 3 1 - 13 \frac{3}{2} i, x = - 3 1 - 13 \frac{1}{2} - 3 1 - 13 \frac{3}{2} i

Graph

Beliebte Beispiele

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