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Beliebt Algebra >

x^7-81x^3=0

Lösung

x^{7} - 81 x^{3} = 0

Lösung

x = 0, x = 3 i, x = - 3 i, x = - 3, x = 3

Schritte zur Lösung

x^{7} - 81 x^{3} = 0

Faktorisiere

x^{7} - 81 x^{3} : x^{3} (x^{2} + 9) (x + 3) (x - 3)

x^{3} (x^{2} + 9) (x + 3) (x - 3) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x = 0 or x^{2} + 9 = 0 or x + 3 = 0 or x - 3 = 0

Löse

x^{2} + 9 = 0 : x = 3 i, x = - 3 i

Löse

x + 3 = 0 : x = - 3

Löse

x - 3 = 0 : x = 3

Die Lösungen sind

x = 0, x = 3 i, x = - 3 i, x = - 3, x = 3

Graph

Beliebte Beispiele

x^3-7x^2+8x+16=0

x^{3} - 7 x^{2} + 8 x + 16 = 0

x^{4} = \frac{1}{81}

x^3+2x^2-5x-10=0

x^{3} + 2 x^{2} - 5 x - 10 = 0

wurzeln von x^4-5x^2+4=0

roo t s x^{4} - 5 x^{2} + 4 = 0

2 x^{3} + 2 x^{2} + 1 = 0