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Beliebt Algebra >

y-y^9=0

Lösung

y - y^{9} = 0

Lösung

y = 0, y = - \frac{2}{2} + i \frac{2}{2}, y = - \frac{2}{2} - i \frac{2}{2}, y = \frac{2}{2} + i \frac{2}{2}, y = \frac{2}{2} - i \frac{2}{2}, y = i, y = - i, y = - 1, y = 1

Schritte zur Lösung

y - y^{9} = 0

Faktorisiere

y - y^{9} : - y (y^{2} + 2 y + 1) (y^{2} - 2 y + 1) (y^{2} + 1) (y + 1) (y - 1)

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

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

Löse

y^{2} + 2 y + 1 = 0 : y = - \frac{2}{2} + i \frac{2}{2}, y = - \frac{2}{2} - i \frac{2}{2}

Löse

y^{2} - 2 y + 1 = 0 : y = \frac{2}{2} + i \frac{2}{2}, y = \frac{2}{2} - i \frac{2}{2}

Löse

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

Löse

y + 1 = 0 : y = - 1

Löse

y - 1 = 0 : y = 1

Die Lösungen sind

y = 0, y = - \frac{2}{2} + i \frac{2}{2}, y = - \frac{2}{2} - i \frac{2}{2}, y = \frac{2}{2} + i \frac{2}{2}, y = \frac{2}{2} - i \frac{2}{2}, y = i, y = - i, y = - 1, y = 1

Graph

Beliebte Beispiele

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