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Beliebt Algebra >

x^6-5x^3-16=0

Lösung

x^{6} - 5 x^{3} - 16 = 0

Lösung

x = 3 \frac{5 + 89}{2}, x = - 3 \frac{5 + 89}{2} \frac{1}{2} + 3 \frac{5 + 89}{2} \frac{3}{2} i, x = - 3 \frac{5 + 89}{2} \frac{1}{2} - 3 \frac{5 + 89}{2} \frac{3}{2} i, x = 3 \frac{5 - 89}{2}, x = - 3 \frac{5 - 89}{2} \frac{1}{2} + 3 \frac{5 - 89}{2} \frac{3}{2} i, x = - 3 \frac{5 - 89}{2} \frac{1}{2} - 3 \frac{5 - 89}{2} \frac{3}{2} i

Schritte zur Lösung

x^{6} - 5 x^{3} - 16 = 0

Schreibe die Gleichung um mit

u = x^{3}

und

u^{2} = x^{6}

u^{2} - 5 u - 16 = 0

Löse

u^{2} - 5 u - 16 = 0 : u = \frac{5 + 89}{2}, u = \frac{5 - 89}{2}

u = \frac{5 + 89}{2}, u = \frac{5 - 89}{2}

Setze

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

löse für

x

Löse

x^{3} = \frac{5 + 89}{2} : x = 3 \frac{5 + 89}{2}, x = - 3 \frac{5 + 89}{2} \frac{1}{2} + 3 \frac{5 + 89}{2} \frac{3}{2} i, x = - 3 \frac{5 + 89}{2} \frac{1}{2} - 3 \frac{5 + 89}{2} \frac{3}{2} i

Löse

x^{3} = \frac{5 - 89}{2} : x = 3 \frac{5 - 89}{2}, x = - 3 \frac{5 - 89}{2} \frac{1}{2} + 3 \frac{5 - 89}{2} \frac{3}{2} i, x = - 3 \frac{5 - 89}{2} \frac{1}{2} - 3 \frac{5 - 89}{2} \frac{3}{2} i

Die Lösungen sind

x = 3 \frac{5 + 89}{2}, x = - 3 \frac{5 + 89}{2} \frac{1}{2} + 3 \frac{5 + 89}{2} \frac{3}{2} i, x = - 3 \frac{5 + 89}{2} \frac{1}{2} - 3 \frac{5 + 89}{2} \frac{3}{2} i, x = 3 \frac{5 - 89}{2}, x = - 3 \frac{5 - 89}{2} \frac{1}{2} + 3 \frac{5 - 89}{2} \frac{3}{2} i, x = - 3 \frac{5 - 89}{2} \frac{1}{2} - 3 \frac{5 - 89}{2} \frac{3}{2} i

Graph

Beliebte Beispiele

(x - 5) \cdot x^{2} = 14

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