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Beliebt Algebra >

24x^4-2x^2-1=0

Lösung

24 x^{4} - 2 x^{2} - 1 = 0

Lösung

x = \frac{1}{2}, x = - \frac{1}{2}, x = \frac{1}{6} i, x = - \frac{1}{6} i

Schritte zur Lösung

24 x^{4} - 2 x^{2} - 1 = 0

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

24 u^{2} - 2 u - 1 = 0

Löse

24 u^{2} - 2 u - 1 = 0 : u = \frac{1}{4}, u = - \frac{1}{6}

u = \frac{1}{4}, u = - \frac{1}{6}

Setze

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

löse für

x

Löse

x^{2} = \frac{1}{4} : x = \frac{1}{2}, x = - \frac{1}{2}

Löse

x^{2} = - \frac{1}{6} : x = \frac{1}{6} i, x = - \frac{1}{6} i

Die Lösungen sind

x = \frac{1}{2}, x = - \frac{1}{2}, x = \frac{1}{6} i, x = - \frac{1}{6} i

Graph

Beliebte Beispiele

x^3+x^2-16x+20=0

x^{3} + x^{2} - 16 x + 20 = 0

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- 3 x + 15 = x^{4} + 3 x^{2} + 5 x + 3

x^{2} (36 - 2 x) = 12

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-x^3+24x^2-56x-96=0

- x^{3} + 24 x^{2} - 56 x - 96 = 0