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Beliebt Algebra >

32x^5-162x=0

Lösung

32 x^{5} - 162 x = 0

Lösung

x = 0, x = \frac{3}{2} i, x = - \frac{3}{2} i, x = - \frac{3}{2}, x = \frac{3}{2}

Schritte zur Lösung

32 x^{5} - 162 x = 0

Faktorisiere

32 x^{5} - 162 x : 2 x (4 x^{2} + 9) (2 x + 3) (2 x - 3)

2 x (4 x^{2} + 9) (2 x + 3) (2 x - 3) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x = 0 or 4 x^{2} + 9 = 0 or 2 x + 3 = 0 or 2 x - 3 = 0

Löse

4 x^{2} + 9 = 0 : x = \frac{3}{2} i, x = - \frac{3}{2} i

Löse

2 x + 3 = 0 : x = - \frac{3}{2}

Löse

2 x - 3 = 0 : x = \frac{3}{2}

Die Lösungen sind

x = 0, x = \frac{3}{2} i, x = - \frac{3}{2} i, x = - \frac{3}{2}, x = \frac{3}{2}

Graph

Beliebte Beispiele

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

k^{3} = 5

x^{4} = 13 x^{2} - 36

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

-x^3+7x^2+17x+9=0

- x^{3} + 7 x^{2} + 17 x + 9 = 0