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Beliebt Algebra >

(x^2-x-3)^2-x^3=17

Lösung

(x^{2} - x - 3)^{2} - x^{3} = 17

Lösung

x = - 2, x = 4, x = \frac{1}{2} + i \frac{3}{2}, x = \frac{1}{2} - i \frac{3}{2}

Schritte zur Lösung

(x^{2} - x - 3)^{2} - x^{3} = 17

Schreibe

(x^{2} - x - 3)^{2} - x^{3}

um:

x^{4} - 3 x^{3} - 5 x^{2} + 6 x + 9

x^{4} - 3 x^{3} - 5 x^{2} + 6 x + 9 = 17

Verschiebe

17

auf die linke Seite

x^{4} - 3 x^{3} - 5 x^{2} + 6 x - 8 = 0

Faktorisiere

x^{4} - 3 x^{3} - 5 x^{2} + 6 x - 8 : (x + 2) (x - 4) (x^{2} - x + 1)

(x + 2) (x - 4) (x^{2} - x + 1) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x + 2 = 0 or x - 4 = 0 or x^{2} - x + 1 = 0

Löse

x + 2 = 0 : x = - 2

Löse

x - 4 = 0 : x = 4

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 = - 2, x = 4, x = \frac{1}{2} + i \frac{3}{2}, x = \frac{1}{2} - i \frac{3}{2}

Graph

Beliebte Beispiele

(2x^2-5)^2=39+10(2x^2-5)

(2 x^{2} - 5)^{2} = 39 + 10 (2 x^{2} - 5)

z^{5} = 14

3x^4-2x^3-27245+69x-9x^2=348062x+2

3 x^{4} - 2 x^{3} - 27245 + 69 x - 9 x^{2} = 348062 x + 2

m^3+2m^2-5m-6=0

m^{3} + 2 m^{2} - 5 m - 6 = 0

2 x^{5} + 36 = 2 x - 6