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Beliebt Algebra >

faktorisieren x^8-17x^4+16=0

Lösung

faktorisieren

x^{8} - 17 x^{4} + 16 = 0

Lösung

x = i, x = - i, x = - 1, x = 1, x = 2 i, x = - 2 i, x = - 2, x = 2

Schritte zur Lösung

x^{8} - 17 x^{4} + 16 = 0

Faktorisiere

x^{8} - 17 x^{4} + 16 : (x^{2} + 1) (x + 1) (x - 1) (x^{2} + 4) (x + 2) (x - 2)

(x^{2} + 1) (x + 1) (x - 1) (x^{2} + 4) (x + 2) (x - 2) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x^{2} + 1 = 0 or x + 1 = 0 or x - 1 = 0 or x^{2} + 4 = 0 or x + 2 = 0 or x - 2 = 0

Löse

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

Löse

x + 1 = 0 : x = - 1

Löse

x - 1 = 0 : x = 1

Löse

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

Löse

x + 2 = 0 : x = - 2

Löse

x - 2 = 0 : x = 2

Die Lösungen sind

x = i, x = - i, x = - 1, x = 1, x = 2 i, x = - 2 i, x = - 2, x = 2

Graph

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