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Beliebt Algebra >

x^5-x^4-x+1=0

Lösung

x^{5} - x^{4} - x + 1 = 0

Lösung

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

Schritte zur Lösung

x^{5} - x^{4} - x + 1 = 0

Faktorisiere

x^{5} - x^{4} - x + 1 : (x - 1)^{2} (x^{2} + 1) (x + 1)

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

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

Löse

x - 1 = 0 : x = 1

Löse

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

Löse

x + 1 = 0 : x = - 1

Die Lösungen sind

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

Graph

Beliebte Beispiele

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

2x^3-x^2-18x+9=0

2 x^{3} - x^{2} - 18 x + 9 = 0

-x^3+5x^2-8x+4=0

- x^{3} + 5 x^{2} - 8 x + 4 = 0

x^{4} = 625

20=[5+(0.12x)/(10)]^{20}

20 = [5 + \frac{0.12 x}{10}]^{20}