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Beliebt Algebra >

x^6+9x^3-5=0

Lösung

x^{6} + 9 x^{3} - 5 = 0

Lösung

x = 3 \frac{- 9 + 101}{2}, x = - 3 \frac{- 9 + 101}{2} \frac{1}{2} + 3 \frac{- 9 + 101}{2} \frac{3}{2} i, x = - 3 \frac{- 9 + 101}{2} \frac{1}{2} - 3 \frac{- 9 + 101}{2} \frac{3}{2} i, x = 3 \frac{- 9 - 101}{2}, x = - 3 \frac{- 9 - 101}{2} \frac{1}{2} + 3 \frac{- 9 - 101}{2} \frac{3}{2} i, x = - 3 \frac{- 9 - 101}{2} \frac{1}{2} - 3 \frac{- 9 - 101}{2} \frac{3}{2} i

Schritte zur Lösung

x^{6} + 9 x^{3} - 5 = 0

Schreibe die Gleichung um mit

u = x^{3}

und

u^{2} = x^{6}

u^{2} + 9 u - 5 = 0

Löse

u^{2} + 9 u - 5 = 0 : u = \frac{- 9 + 101}{2}, u = \frac{- 9 - 101}{2}

u = \frac{- 9 + 101}{2}, u = \frac{- 9 - 101}{2}

Setze

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

löse für

x

Löse

x^{3} = \frac{- 9 + 101}{2} : x = 3 \frac{- 9 + 101}{2}, x = - 3 \frac{- 9 + 101}{2} \frac{1}{2} + 3 \frac{- 9 + 101}{2} \frac{3}{2} i, x = - 3 \frac{- 9 + 101}{2} \frac{1}{2} - 3 \frac{- 9 + 101}{2} \frac{3}{2} i

Löse

x^{3} = \frac{- 9 - 101}{2} : x = 3 \frac{- 9 - 101}{2}, x = - 3 \frac{- 9 - 101}{2} \frac{1}{2} + 3 \frac{- 9 - 101}{2} \frac{3}{2} i, x = - 3 \frac{- 9 - 101}{2} \frac{1}{2} - 3 \frac{- 9 - 101}{2} \frac{3}{2} i

Die Lösungen sind

x = 3 \frac{- 9 + 101}{2}, x = - 3 \frac{- 9 + 101}{2} \frac{1}{2} + 3 \frac{- 9 + 101}{2} \frac{3}{2} i, x = - 3 \frac{- 9 + 101}{2} \frac{1}{2} - 3 \frac{- 9 + 101}{2} \frac{3}{2} i, x = 3 \frac{- 9 - 101}{2}, x = - 3 \frac{- 9 - 101}{2} \frac{1}{2} + 3 \frac{- 9 - 101}{2} \frac{3}{2} i, x = - 3 \frac{- 9 - 101}{2} \frac{1}{2} - 3 \frac{- 9 - 101}{2} \frac{3}{2} i

Graph

Beliebte Beispiele

2 x^{3} - x + 12 = x^{4}

4x^3-12x^2+9x=0

4 x^{3} - 12 x^{2} + 9 x = 0

0.16 = (1 + x)^{3} - 1

4 t^{3} + 6 t + 2.5 = 25

3 x^{2} \cdot 2 x = 162