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Beliebt Algebra >

x^6+13x^4+36x^2=0

Lösung

x^{6} + 13 x^{4} + 36 x^{2} = 0

Lösung

x = 0, x = 2 i, x = - 2 i, x = 3 i, x = - 3 i

Schritte zur Lösung

x^{6} + 13 x^{4} + 36 x^{2} = 0

Schreibe die Gleichung um mit

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

und

u^{3} = x^{6}

u^{3} + 13 u^{2} + 36 u = 0

Löse

u^{3} + 13 u^{2} + 36 u = 0 : u = 0, u = - 4, u = - 9

u = 0, u = - 4, u = - 9

Setze

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

löse für

x

Löse

x^{2} = 0 : x = 0

Löse

x^{2} = - 4 : x = 2 i, x = - 2 i

Löse

x^{2} = - 9 : x = 3 i, x = - 3 i

Die Lösungen sind

x = 0, x = 2 i, x = - 2 i, x = 3 i, x = - 3 i

Graph

Beliebte Beispiele

7x^5-33x^4-4x^2+3x+52=0

7 x^{5} - 33 x^{4} - 4 x^{2} + 3 x + 52 = 0

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