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Beliebt Algebra >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Faktorisiere

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

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

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

Löse

x - 1 = 0 : x = 1

Löse

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

Löse

x + 2 = 0 : x = - 2

Löse

x - 2 = 0 : x = 2

Die Lösungen sind

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

Graph

Beliebte Beispiele

solvefor y,4x^3-16y=4y^3-16x

so l v e f or y, 4 x^{3} - 16 y = 4 y^{3} - 16 x

4 x^{7} - 64 x^{3} = 0

5t^4+15t^2+50=0

5 t^{4} + 15 t^{2} + 50 = 0

- 4 x^{3} + 24 x = 0

4 x^{3} + 24 x + 36 = 0