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Beliebt Algebra >

x^8+x^7+x^6+x^5+x^4+x^3+x^2+x=0

Lösung

x^{8} + x^{7} + x^{6} + x^{5} + x^{4} + x^{3} + x^{2} + x = 0

Lösung

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

Schritte zur Lösung

x^{8} + x^{7} + x^{6} + x^{5} + x^{4} + x^{3} + x^{2} + x = 0

Faktorisiere

x^{8} + x^{7} + x^{6} + x^{5} + x^{4} + x^{3} + x^{2} + x : x (x + 1) (x^{2} + 1) (x^{2} + 2 x + 1) (x^{2} - 2 x + 1)

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

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

Löse

x + 1 = 0 : x = - 1

Löse

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

Löse

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

Löse

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

Die Lösungen sind

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

Graph

Beliebte Beispiele

x^3-6x^2+11x+6=0

x^{3} - 6 x^{2} + 11 x + 6 = 0

x^{3} = 27 x^{10}

x^{3} x + 1 x = \frac{2}{3}

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

y^{4} - 18 y^{2} + 81 = 0