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Beliebt Algebra >

(x-1)(x+1)(x+3)(x+5)+15=0

Lösung

(x - 1) (x + 1) (x + 3) (x + 5) + 15 = 0

Lösung

x = 0, x = - 4, x = - 2 + 6, x = - 2 - 6

+1

Dezimale

x = 0, x = - 4, x = 0.44948 \dots, x = - 4.44948 \dots

Schritte zur Lösung

(x - 1) (x + 1) (x + 3) (x + 5) + 15 = 0

Schreibe

(x - 1) (x + 1) (x + 3) (x + 5) + 15

um:

x^{4} + 8 x^{3} + 14 x^{2} - 8 x

x^{4} + 8 x^{3} + 14 x^{2} - 8 x = 0

Faktorisiere

x^{4} + 8 x^{3} + 14 x^{2} - 8 x : x (x + 4) (x^{2} + 4 x - 2)

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

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

Löse

x + 4 = 0 : x = - 4

Löse

x^{2} + 4 x - 2 = 0 : x = - 2 + 6, x = - 2 - 6

Die Lösungen sind

x = 0, x = - 4, x = - 2 + 6, x = - 2 - 6

Graph

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x^{3} - 7 x^{2} + 8 x + 10 = 0

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(m^2+1)^3(m^2+m+1)^2=0

(m^{2} + 1)^{3} (m^{2} + m + 1)^{2} = 0