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Beliebt Algebra >

x^6-2sqrt(3)x^4+4x^2=0

Lösung

x^{6} - 23 x^{4} + 4 x^{2} = 0

Lösung

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

Schritte zur Lösung

x^{6} - 23 x^{4} + 4 x^{2} = 0

Schreibe die Gleichung um mit

u = x^{2}, u^{2} = x^{4}

und

u^{3} = x^{6}

u^{3} - 23 u^{2} + 4 u = 0

Löse

u^{3} - 23 u^{2} + 4 u = 0 : u = 0, u = 3 + i, u = 3 - i

u = 0, u = 3 + i, u = 3 - i

Setze

u = x^{2} w i e d er e in,

löse für

x

Löse

x^{2} = 0 : x = 0

Löse

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

Löse

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

Die Lösungen sind

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

Graph

Beliebte Beispiele

y^{3} + 3 y^{2} = 4 y + 12

x^4+2x^3-5x^2-4x+6=0

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

8 x^{3} - 1 = 0

w^{3} = i

z^{3} = \frac{i}{8}