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Beliebt Algebra >

x^7+7x^4-8x=0

Lösung

x^{7} + 7 x^{4} - 8 x = 0

Lösung

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

Schritte zur Lösung

x^{7} + 7 x^{4} - 8 x = 0

Faktorisiere

x^{7} + 7 x^{4} - 8 x : x (x - 1) (x + 2) (x^{2} + x + 1) (x^{2} - 2 x + 4)

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

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

Löse

x - 1 = 0 : x = 1

Löse

x + 2 = 0 : x = - 2

Löse

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

Löse

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

Die Lösungen sind

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

Graph

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