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Beliebt Algebra >

x^4-5x^3+8x^2-5x+1=0

Lösung

x^{4} - 5 x^{3} + 8 x^{2} - 5 x + 1 = 0

Lösung

x = 1, x = \frac{3 + 5}{2}, x = \frac{3 - 5}{2}

+1

Dezimale

x = 1, x = 2.61803 \dots, x = 0.38196 \dots

Schritte zur Lösung

x^{4} - 5 x^{3} + 8 x^{2} - 5 x + 1 = 0

Faktorisiere

x^{4} - 5 x^{3} + 8 x^{2} - 5 x + 1 : (x - 1)^{2} (x^{2} - 3 x + 1)

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

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

Löse

x - 1 = 0 : x = 1

Löse

x^{2} - 3 x + 1 = 0 : x = \frac{3 + 5}{2}, x = \frac{3 - 5}{2}

Die Lösungen sind

x = 1, x = \frac{3 + 5}{2}, x = \frac{3 - 5}{2}

Graph

Beliebte Beispiele

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

-3x^5-7x^4+x^3+7x^2+2x=0

- 3 x^{5} - 7 x^{4} + x^{3} + 7 x^{2} + 2 x = 0

x^{7} - 7 x - 2 = 0

x^3-7x^2+11x-5=0

x^{3} - 7 x^{2} + 11 x - 5 = 0

z^{3} = - i