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Beliebt Algebra >

x^6-6x^4+8x^2=0

Lösung

x^{6} - 6 x^{4} + 8 x^{2} = 0

Lösung

x = 0, x = 2, x = - 2, x = 2, x = - 2

+1

Dezimale

x = 0, x = 1.41421 \dots, x = - 1.41421 \dots, x = 2, x = - 2

Schritte zur Lösung

x^{6} - 6 x^{4} + 8 x^{2} = 0

Schreibe die Gleichung um mit

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

und

u^{3} = x^{6}

u^{3} - 6 u^{2} + 8 u = 0

Löse

u^{3} - 6 u^{2} + 8 u = 0 : u = 0, u = 2, u = 4

u = 0, u = 2, u = 4

Setze

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

löse für

x

Löse

x^{2} = 0 : x = 0

Löse

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

Löse

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

Die Lösungen sind

x = 0, x = 2, x = - 2, x = 2, x = - 2

Graph

Beliebte Beispiele

y^{4} - 5 y^{2} + 6 = 0

x^{3} - 2 x^{2} - 4 x = - 8

x^3-9x^2+15x-7=0

x^{3} - 9 x^{2} + 15 x - 7 = 0

5 + x^{4} = 1

6p^3+7p^2=96p+112

6 p^{3} + 7 p^{2} = 96 p + 112