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Beliebt Algebra >

x(x^3-1)=0

Lösung

x (x^{3} - 1) = 0

Lösung

x = 0, x = 1, x = - \frac{1}{2} + i \frac{3}{2}, x = - \frac{1}{2} - i \frac{3}{2}

Schritte zur Lösung

x (x^{3} - 1) = 0

Faktorisiere

x (x^{3} - 1) : x (x - 1) (x^{2} + x + 1)

x (x - 1) (x^{2} + x + 1) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x = 0 or x - 1 = 0 or x^{2} + x + 1 = 0

Löse

x - 1 = 0 : x = 1

Löse

x^{2} + x + 1 = 0 : x = - \frac{1}{2} + i \frac{3}{2}, x = - \frac{1}{2} - i \frac{3}{2}

Die Lösungen sind

x = 0, x = 1, x = - \frac{1}{2} + i \frac{3}{2}, x = - \frac{1}{2} - i \frac{3}{2}

Graph

Beliebte Beispiele

8 x^{3} - 50 x = 0

k^3-4k^2-2k+8=0

k^{3} - 4 k^{2} - 2 k + 8 = 0

x^{3} = 3 x^{2}

2x^3-24x^2+64x=0

2 x^{3} - 24 x^{2} + 64 x = 0

x^3+4x^2+8x+10=0

x^{3} + 4 x^{2} + 8 x + 10 = 0