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Beliebt Algebra >

4x^5-x^3-4x^2+1=0

Lösung

4 x^{5} - x^{3} - 4 x^{2} + 1 = 0

Lösung

x = - \frac{1}{2}, x = \frac{1}{2}, x = 1, x = - \frac{1}{2} + i \frac{3}{2}, x = - \frac{1}{2} - i \frac{3}{2}

Schritte zur Lösung

4 x^{5} - x^{3} - 4 x^{2} + 1 = 0

Faktorisiere

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

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

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

Löse

2 x + 1 = 0 : x = - \frac{1}{2}

Löse

2 x - 1 = 0 : x = \frac{1}{2}

Löse

x - 1 = 0 : x = 1

Löse

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

Die Lösungen sind

x = - \frac{1}{2}, x = \frac{1}{2}, x = 1, x = - \frac{1}{2} + i \frac{3}{2}, x = - \frac{1}{2} - i \frac{3}{2}

Graph

Beliebte Beispiele

x^{4} - 5 x^{2} - 44 = 0

(x - 5)^{3} = 1

(x-5)^4-(5-x)^2=0

(x - 5)^{4} - (5 - x)^{2} = 0

x^{4} - 5 x^{2} = 4

t^{3} + 2 t = 400