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Beliebt Algebra >

x^7-x^4-x^3+1=0

Lösung

x^{7} - x^{4} - x^{3} + 1 = 0

Lösung

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

Schritte zur Lösung

x^{7} - x^{4} - x^{3} + 1 = 0

Faktorisiere

x^{7} - x^{4} - x^{3} + 1 : (x - 1)^{2} (x^{2} + x + 1) (x^{2} + 1) (x + 1)

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

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

Löse

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

Löse

x + 1 = 0 : x = - 1

Die Lösungen sind

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

Graph

Beliebte Beispiele

x^{3} - 75 x - 250 = 0

12 x^{3} - 3 x^{2} = 0

2 x^{4} = 9 x^{2}

z^{6} - 2 z^{3} + 2 = 0

wurzeln von z^{10}=9^{10}

roo t s z^{10} = 9^{10}