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Beliebt Algebra >

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

Lösung

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

Lösung

x = - 3 + 23, x = - - 3 + 23, x = 3 + 23 i, x = - 3 + 23 i

Schritte zur Lösung

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

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

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

Löse

u^{2} + 6 u - 3 = 0 : u = - 3 + 23, u = - 3 - 23

u = - 3 + 23, u = - 3 - 23

Setze

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

löse für

x

Löse

x^{2} = - 3 + 23 : x = - 3 + 23, x = - - 3 + 23

Löse

x^{2} = - 3 - 23 : x = 3 + 23 i, x = - 3 + 23 i

Die Lösungen sind

x = - 3 + 23, x = - - 3 + 23, x = 3 + 23 i, x = - 3 + 23 i

Graph

Beliebte Beispiele

-x^3+5x^2+25x-125=0

- x^{3} + 5 x^{2} + 25 x - 125 = 0

z^{3} = - 1 - i

x^{2} (x + 3) = 0

solvefor y,(y-x)^3=Cx

so l v e f or y, (y - x)^{3} = C x

x^3+3x^2-36x-108=0

x^{3} + 3 x^{2} - 36 x - 108 = 0