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Beliebt Algebra >

x^4-2x^3+8x-16=0

Lösung

x^{4} - 2 x^{3} + 8 x - 16 = 0

Lösung

x = 2, x = - 2, x = 1 + 3 i, x = 1 - 3 i

Schritte zur Lösung

x^{4} - 2 x^{3} + 8 x - 16 = 0

Faktorisiere

x^{4} - 2 x^{3} + 8 x - 16 : (x - 2) (x + 2) (x^{2} - 2 x + 4)

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

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

Löse

x - 2 = 0 : x = 2

Löse

x + 2 = 0 : x = - 2

Löse

x^{2} - 2 x + 4 = 0 : x = 1 + 3 i, x = 1 - 3 i

Die Lösungen sind

x = 2, x = - 2, x = 1 + 3 i, x = 1 - 3 i

Graph

Beliebte Beispiele

z^{6} = - 8

solvefor y,x=y^4-y^2

so l v e f or y, x = y^{4} - y^{2}

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

x^4+x^3-5x^2+x-6=0

x^{4} + x^{3} - 5 x^{2} + x - 6 = 0

x^{8} + 63 x^{4} = 64