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Beliebt Algebra >

x^6+3x^2=0

Lösung

x^{6} + 3 x^{2} = 0

Lösung

x = 0, x = \frac{4 3}{2} + \frac{4 3}{2} i, x = - \frac{4 3}{2} - \frac{4 3}{2} i, x = \frac{4 3}{2} - \frac{4 3}{2} i, x = - \frac{4 3}{2} + \frac{4 3}{2} i

Schritte zur Lösung

x^{6} + 3 x^{2} = 0

Schreibe die Gleichung um mit

u = x^{2}

und

u^{3} = x^{6}

u^{3} + 3 u = 0

Löse

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

Löse

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

Die Lösungen sind

x = 0, x = \frac{4 3}{2} + \frac{4 3}{2} i, x = - \frac{4 3}{2} - \frac{4 3}{2} i, x = \frac{4 3}{2} - \frac{4 3}{2} i, x = - \frac{4 3}{2} + \frac{4 3}{2} i

Graph

Beliebte Beispiele

- x^{4} + 1 = 0

r^{3} + r = 0

26.28=0.15x^3+0.3x^2

26.28 = 0.15 x^{3} + 0.3 x^{2}

x^4+14x^3+77x^2+200x+208=0

x^{4} + 14 x^{3} + 77 x^{2} + 200 x + 208 = 0

wurzeln von 2.5x^4+3x^3-2.6x^2-5.1x-5.6

roo t s 2.5 x^{4} + 3 x^{3} - 2.6 x^{2} - 5.1 x - 5.6