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Beliebt Algebra >

(x^2+3x)^2-2(x^2+3x)-8=0

Lösung

(x^{2} + 3 x)^{2} - 2 (x^{2} + 3 x) - 8 = 0

Lösung

x = - 1, x = 1, x = - 2, x = - 4

Schritte zur Lösung

(x^{2} + 3 x)^{2} - 2 (x^{2} + 3 x) - 8 = 0

Schreibe

(x^{2} + 3 x)^{2} - 2 (x^{2} + 3 x) - 8

um:

x^{4} + 6 x^{3} + 7 x^{2} - 6 x - 8

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

Faktorisiere

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

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x + 1 = 0 or x - 1 = 0 or x + 2 = 0 or x + 4 = 0

Löse

x + 1 = 0 : x = - 1

Löse

x - 1 = 0 : x = 1

Löse

x + 2 = 0 : x = - 2

Löse

x + 4 = 0 : x = - 4

Die Lösungen sind

x = - 1, x = 1, x = - 2, x = - 4

Graph

Beliebte Beispiele

216 x = x^{4}

4 x^{4} = 10

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

1 - 3 x + 3 x^{2} - x^{3} = 0

-x^3-35x^2+3150x+104000=0

- x^{3} - 35 x^{2} + 3150 x + 104000 = 0

16 x^{4} + 36 = 52 x^{2}