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Beliebt Algebra >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Faktorisiere

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

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

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

Löse

x + 1 = 0 : x = - 1

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}

Die Lösungen sind

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

Graph

Beliebte Beispiele

2-15x+9x^2-x^3=0

2 - 15 x + 9 x^{2} - x^{3} = 0

x^4+2x^3=x^2+2x

x^{4} + 2 x^{3} = x^{2} + 2 x

x (9 + x) (x - 2) = 4

x^4-5x^2-10x-6=0

x^{4} - 5 x^{2} - 10 x - 6 = 0

100x^3-45x^2-58x+24=0

100 x^{3} - 45 x^{2} - 58 x + 24 = 0