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Beliebt Algebra >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Schreibe

(x^{2} - x - 3)^{2} - 2 (x^{2} - x) + 3

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

10 = x^{10}

r^{4} + 1 = 0

a x^{4} = 4

2x^3+4x^2+13x+6=0

2 x^{3} + 4 x^{2} + 13 x + 6 = 0

(t + 1)^{5} = - 243