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Beliebt Algebra >

(x^2+2x)^2-5(x^2+2x)+6=0

Lösung

(x^{2} + 2 x)^{2} - 5 (x^{2} + 2 x) + 6 = 0

Lösung

x = 1, x = - 3, x = - 1 + 3, x = - 1 - 3

+1

Dezimale

x = 1, x = - 3, x = 0.73205 \dots, x = - 2.73205 \dots

Schritte zur Lösung

(x^{2} + 2 x)^{2} - 5 (x^{2} + 2 x) + 6 = 0

Schreibe

(x^{2} + 2 x)^{2} - 5 (x^{2} + 2 x) + 6

um:

x^{4} + 4 x^{3} - x^{2} - 10 x + 6

x^{4} + 4 x^{3} - x^{2} - 10 x + 6 = 0

Faktorisiere

x^{4} + 4 x^{3} - x^{2} - 10 x + 6 : (x - 1) (x + 3) (x^{2} + 2 x - 2)

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

Löse

x - 1 = 0 : x = 1

Löse

x + 3 = 0 : x = - 3

Löse

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

Die Lösungen sind

x = 1, x = - 3, x = - 1 + 3, x = - 1 - 3

Graph

Beliebte Beispiele

solvefor a,a^4b+2c^5=d^1e

so l v e f or a, a^{4} b + 2 c^{5} = d^{1} e

8m^3-104m^2+336m=0

8 m^{3} - 104 m^{2} + 336 m = 0

5 x^{3} - 29 x + 30 = 0

-x^3+3x^2-24x+1=0

- x^{3} + 3 x^{2} - 24 x + 1 = 0

x^3-8x^2+21x-18x=0

x^{3} - 8 x^{2} + 21 x - 18 x = 0