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Beliebt Algebra >

x^2(x^2-4)=x^4(x^2-4)

Lösung

x^{2} (x^{2} - 4) = x^{4} (x^{2} - 4)

Lösung

x = 0, x = - 2, x = 2, x = - 1, x = 1

Schritte zur Lösung

x^{2} (x^{2} - 4) = x^{4} (x^{2} - 4)

Verschiebe

x^{4} (x^{2} - 4)

auf die linke Seite

x^{2} (x^{2} - 4) - x^{4} (x^{2} - 4) = 0

Faktorisiere

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

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

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

Löse

x + 2 = 0 : x = - 2

Löse

x - 2 = 0 : x = 2

Löse

x + 1 = 0 : x = - 1

Löse

x - 1 = 0 : x = 1

Die Lösungen sind

x = 0, x = - 2, x = 2, x = - 1, x = 1

Graph

Beliebte Beispiele

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

x^3-x^2-x-25=470

x^{3} - x^{2} - x - 25 = 470

-x^3-x^2+8x+12=0

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

2a^2(a^2+2)=27+7a^2

2 a^{2} (a^{2} + 2) = 27 + 7 a^{2}

2 x - 53 = 2 + x^{15}