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Beliebt Algebra >

x^6+28x^3+27=0

Lösung

x^{6} + 28 x^{3} + 27 = 0

Lösung

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

Schritte zur Lösung

x^{6} + 28 x^{3} + 27 = 0

Schreibe die Gleichung um mit

u = x^{3}

und

u^{2} = x^{6}

u^{2} + 28 u + 27 = 0

Löse

u^{2} + 28 u + 27 = 0 : u = - 1, u = - 27

u = - 1, u = - 27

Setze

u = x^{3} w i e d er e in,

löse für

x

Löse

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

Löse

x^{3} = - 27 : x = - 3, x = \frac{3}{2} - \frac{3 3}{2} i, x = \frac{3}{2} + \frac{3 3}{2} i

Die Lösungen sind

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

Graph

Beliebte Beispiele

x(2x^2)=-2x^2+x-2

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

x^{4} = 26 x^{2} - 25

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

x^{4} + x - 3 = 0

y^{3} + 81 = 36 y