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Beliebt Algebra >

(x^2+x)^2-8(x^2+x)+12=0

Lösung

(x^{2} + x)^{2} - 8 (x^{2} + x) + 12 = 0

Lösung

x = 1, x = - 3, x = - 2, x = 2

Schritte zur Lösung

(x^{2} + x)^{2} - 8 (x^{2} + x) + 12 = 0

Schreibe

(x^{2} + x)^{2} - 8 (x^{2} + x) + 12

um:

x^{4} + 2 x^{3} - 7 x^{2} - 8 x + 12

x^{4} + 2 x^{3} - 7 x^{2} - 8 x + 12 = 0

Faktorisiere

x^{4} + 2 x^{3} - 7 x^{2} - 8 x + 12 : (x - 1) (x + 3) (x + 2) (x - 2)

(x - 1) (x + 3) (x + 2) (x - 2) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x - 1 = 0 or x + 3 = 0 or x + 2 = 0 or x - 2 = 0

Löse

x - 1 = 0 : x = 1

Löse

x + 3 = 0 : x = - 3

Löse

x + 2 = 0 : x = - 2

Löse

x - 2 = 0 : x = 2

Die Lösungen sind

x = 1, x = - 3, x = - 2, x = 2

Graph

Beliebte Beispiele

725 = 5 x^{3}

27 x^{3} = 8

2x^3-3x^2-12x=0

2 x^{3} - 3 x^{2} - 12 x = 0

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

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

x^5-4x^4-12x^3=0

x^{5} - 4 x^{4} - 12 x^{3} = 0