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Beliebt Algebra >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Schreibe

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

um:

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

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

Faktorisiere

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

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

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

Löse

x - 1 = 0 : x = 1

Löse

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

Die Lösungen sind

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

Graph

Beliebte Beispiele

216 = 1 r^{4 - 1}

x^3-2x^2+2x+4=0

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

(49x^2-4)(x^2-7)=0

(49 x^{2} - 4) (x^{2} - 7) = 0

x^{2} + x^{3} - 5 x = 0

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