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Beliebt Algebra >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Faktorisiere

x^{5} + 3 x^{3} - 4 x : x (x + 1) (x - 1) (x^{2} + 4)

x (x + 1) (x - 1) (x^{2} + 4) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x = 0 or x + 1 = 0 or x - 1 = 0 or x^{2} + 4 = 0

Löse

x + 1 = 0 : x = - 1

Löse

x - 1 = 0 : x = 1

Löse

x^{2} + 4 = 0 : x = 2 i, x = - 2 i

Die Lösungen sind

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

Graph

Beliebte Beispiele

r^3-7r^2+16r-12=0

r^{3} - 7 r^{2} + 16 r - 12 = 0

x^{3} + 3 x^{2} - 112 = 0

x^4-6/7 x^2+3/35 =0

x^{4} - \frac{6}{7} x^{2} + \frac{3}{35} = 0

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

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

5 x^{4} + 7 x^{2} - 12 = 0