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Beliebt Algebra >

x^7-28x^4+27x=0

Lösung

x^{7} - 28 x^{4} + 27 x = 0

Lösung

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

Schritte zur Lösung

x^{7} - 28 x^{4} + 27 x = 0

Faktorisiere

x^{7} - 28 x^{4} + 27 x : x (x - 1) (x - 3) (x^{2} + x + 1) (x^{2} + 3 x + 9)

x (x - 1) (x - 3) (x^{2} + x + 1) (x^{2} + 3 x + 9) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x = 0 or x - 1 = 0 or x - 3 = 0 or x^{2} + x + 1 = 0 or x^{2} + 3 x + 9 = 0

Löse

x - 1 = 0 : x = 1

Löse

x - 3 = 0 : x = 3

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

Die Lösungen sind

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

Graph

Beliebte Beispiele

x^{3} = 5 x^{2}

18x^3-27x^2-50x+75=0

18 x^{3} - 27 x^{2} - 50 x + 75 = 0

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

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

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

x^3-4x^2+20x-77=0

x^{3} - 4 x^{2} + 20 x - 77 = 0