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Beliebt Algebra >

12x^4-x^2-1=0

Lösung

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

Lösung

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

Schritte zur Lösung

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

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

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

Löse

12 u^{2} - u - 1 = 0 : u = \frac{1}{3}, u = - \frac{1}{4}

u = \frac{1}{3}, u = - \frac{1}{4}

Setze

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

löse für

x

Löse

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

Löse

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

Die Lösungen sind

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

Graph

Beliebte Beispiele

x^{4} - 7 x^{2} - 144 = 0

125 x = 5 x^{3}

2x^3+x^2-12x-3=0

2 x^{3} + x^{2} - 12 x - 3 = 0

x^{3} = 400

(12 x^{2} + 1)^{2} = 0