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Beliebt Algebra >

x^6-9x^3+14=0

Lösung

x^{6} - 9 x^{3} + 14 = 0

Lösung

x = 37, x = - 37 \frac{1}{2} + 37 \frac{3}{2} i, x = - 37 \frac{1}{2} - 37 \frac{3}{2} i, x = 32, x = - 32 \frac{1}{2} + 32 \frac{3}{2} i, x = - 32 \frac{1}{2} - 32 \frac{3}{2} i

Schritte zur Lösung

x^{6} - 9 x^{3} + 14 = 0

Schreibe die Gleichung um mit

u = x^{3}

und

u^{2} = x^{6}

u^{2} - 9 u + 14 = 0

Löse

u^{2} - 9 u + 14 = 0 : u = 7, u = 2

u = 7, u = 2

Setze

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

löse für

x

Löse

x^{3} = 7 : x = 37, x = - 37 \frac{1}{2} + 37 \frac{3}{2} i, x = - 37 \frac{1}{2} - 37 \frac{3}{2} i

Löse

x^{3} = 2 : x = 32, x = - 32 \frac{1}{2} + 32 \frac{3}{2} i, x = - 32 \frac{1}{2} - 32 \frac{3}{2} i

Die Lösungen sind

x = 37, x = - 37 \frac{1}{2} + 37 \frac{3}{2} i, x = - 37 \frac{1}{2} - 37 \frac{3}{2} i, x = 32, x = - 32 \frac{1}{2} + 32 \frac{3}{2} i, x = - 32 \frac{1}{2} - 32 \frac{3}{2} i

Graph

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