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Beliebt Algebra >

x^7+x^4+x^3+1=0

Lösung

x^{7} + x^{4} + x^{3} + 1 = 0

Lösung

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

Schritte zur Lösung

x^{7} + x^{4} + x^{3} + 1 = 0

Faktorisiere

x^{7} + x^{4} + x^{3} + 1 : (x + 1) (x^{2} - x + 1) (x^{2} + 2 x + 1) (x^{2} - 2 x + 1)

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

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

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}

Löse

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

Löse

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

Die Lösungen sind

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

Graph

Beliebte Beispiele

(4x-12)^{10}=0^{10}

(4 x - 12)^{10} = 0^{10}

(8x^2)(5x^3)=40x

(8 x^{2}) (5 x^{3}) = 40 x

x^4+8x^3+30x^2+56x-95=0

x^{4} + 8 x^{3} + 30 x^{2} + 56 x - 95 = 0

14.93(x+1)^3=20

14.93 (x + 1)^{3} = 20

x^{4} = 4