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Beliebt Algebra >

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

Lösung

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

Lösung

x = - 1, x = - 5, x = i, x = - i

Schritte zur Lösung

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

Faktorisiere

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

(x + 1) (x + 5) (x^{2} + 1) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x + 1 = 0 or x + 5 = 0 or x^{2} + 1 = 0

Löse

x + 1 = 0 : x = - 1

Löse

x + 5 = 0 : x = - 5

Löse

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

Die Lösungen sind

x = - 1, x = - 5, x = i, x = - i

Graph

Beliebte Beispiele

solvefor a,a^5=b^4

so l v e f or a, a^{5} = b^{4}

x^{3} - x + 1 = 0

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

(x+1)(x+2)^2(x+4)-2x^2=0

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

4 x^{4} - 17 x^{2} + 4 = 0