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Beliebt Algebra >

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

Lösung

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

Lösung

x = 1, x = 3, x = i, x = - i

Schritte zur Lösung

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

Schreibe in der Standard Form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

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

Faktorisiere

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

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

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

Löse

x - 1 = 0 : x = 1

Löse

x - 3 = 0 : x = 3

Löse

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

Die Lösungen sind

x = 1, x = 3, x = i, x = - i

Graph

Beliebte Beispiele

x^{5} = 2

solvefor x,3x^3+2y=10

so l v e f or x, 3 x^{3} + 2 y = 10

x^{3} - 15 x^{2} = 0

36x^4+29x^2-7=0

36 x^{4} + 29 x^{2} - 7 = 0

w (w - 6)^{2} = 0