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Beliebt Algebra >

x^7-64x=0

Lösung

x^{7} - 64 x = 0

Lösung

x = 0, x = - 2, x = 2, x = 1 + 3 i, x = - 1 - 3 i, x = 1 - 3 i, x = - 1 + 3 i

Schritte zur Lösung

x^{7} - 64 x = 0

Faktorisiere

x^{7} - 64 x : x (x + 2) (x - 2) (x^{4} + 4 x^{2} + 16)

x (x + 2) (x - 2) (x^{4} + 4 x^{2} + 16) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x = 0 or x + 2 = 0 or x - 2 = 0 or x^{4} + 4 x^{2} + 16 = 0

Löse

x + 2 = 0 : x = - 2

Löse

x - 2 = 0 : x = 2

Löse

x^{4} + 4 x^{2} + 16 = 0 : x = 1 + 3 i, x = - 1 - 3 i, x = 1 - 3 i, x = - 1 + 3 i

Die Lösungen sind

x = 0, x = - 2, x = 2, x = 1 + 3 i, x = - 1 - 3 i, x = 1 - 3 i, x = - 1 + 3 i

Graph

Beliebte Beispiele

x^{5} - x^{2} = 0

a^{3} + a^{2} = 36

45 = 4 y^{3} - 3

x^4-3x^3-9x^2+23x-12=0

x^{4} - 3 x^{3} - 9 x^{2} + 23 x - 12 = 0

x^3+5x^2-9x-45=0

x^{3} + 5 x^{2} - 9 x - 45 = 0