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Beliebt Algebra >

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

Lösung

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

Lösung

x = - 1, x = 1, x = 2 i, x = - 2 i, x = - 2, x = 2

Schritte zur Lösung

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

Faktorisiere

(x^{2} + 2) (x^{2} - 2) (x^{2} - 1) : (x + 1) (x - 1) (x^{2} + 2) (x + 2) (x - 2)

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

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

Löse

x + 1 = 0 : x = - 1

Löse

x - 1 = 0 : x = 1

Löse

x^{2} + 2 = 0 : x = 2 i, x = - 2 i

Löse

x + 2 = 0 : x = - 2

Löse

x - 2 = 0 : x = 2

Die Lösungen sind

x = - 1, x = 1, x = 2 i, x = - 2 i, x = - 2, x = 2

Graph

Beliebte Beispiele

x^6+x^4-10x+8=0

x^{6} + x^{4} - 10 x + 8 = 0

3y^3-23y^2-8y=0

3 y^{3} - 23 y^{2} - 8 y = 0

solvefor x,x^4+y^4=17

so l v e f or x, x^{4} + y^{4} = 17

k^{3} = 216

2y^2(y^2-2)=18+y^2

2 y^{2} (y^{2} - 2) = 18 + y^{2}