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Beliebt Algebra >

x^5+x^4+x^3+x^2+x+1=0

Lösung

x^{5} + x^{4} + x^{3} + x^{2} + x + 1 = 0

Lösung

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

Schritte zur Lösung

x^{5} + x^{4} + x^{3} + x^{2} + x + 1 = 0

Faktorisiere

x^{5} + x^{4} + x^{3} + x^{2} + x + 1 : (x^{2} + x + 1) (x + 1) (x^{2} - x + 1)

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

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

Löse

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

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

Graph

Beliebte Beispiele

2x^3-8x^2=8x-32

2 x^{3} - 8 x^{2} = 8 x - 32

x^{3} - 36 x = 0

z^{3} = 27 i

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

0=x^3-4x^2-9x+36

0 = x^{3} - 4 x^{2} - 9 x + 36