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Beliebt Algebra >

54x^4-3x^2-1=0

Lösung

54 x^{4} - 3 x^{2} - 1 = 0

Lösung

x = \frac{1}{6}, x = - \frac{1}{6}, x = \frac{1}{3} i, x = - \frac{1}{3} i

Schritte zur Lösung

54 x^{4} - 3 x^{2} - 1 = 0

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

54 u^{2} - 3 u - 1 = 0

Löse

54 u^{2} - 3 u - 1 = 0 : u = \frac{1}{6}, u = - \frac{1}{9}

u = \frac{1}{6}, u = - \frac{1}{9}

Setze

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

löse für

x

Löse

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

Löse

x^{2} = - \frac{1}{9} : x = \frac{1}{3} i, x = - \frac{1}{3} i

Die Lösungen sind

x = \frac{1}{6}, x = - \frac{1}{6}, x = \frac{1}{3} i, x = - \frac{1}{3} i

Graph

Beliebte Beispiele

2x^4-x^3-2x+23x=-2

2 x^{4} - x^{3} - 2 x + 23 x = - 2

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x^{4} - 48 x^{2} + 512 = 0

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

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