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Beliebt Algebra >

4x^4-12x^2-7=0

Lösung

4 x^{4} - 12 x^{2} - 7 = 0

Lösung

x = \frac{7}{2}, x = - \frac{7}{2}, x = \frac{1}{2} i, x = - \frac{1}{2} i

Schritte zur Lösung

4 x^{4} - 12 x^{2} - 7 = 0

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

4 u^{2} - 12 u - 7 = 0

Löse

4 u^{2} - 12 u - 7 = 0 : u = \frac{7}{2}, u = - \frac{1}{2}

u = \frac{7}{2}, u = - \frac{1}{2}

Setze

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

löse für

x

Löse

x^{2} = \frac{7}{2} : x = \frac{7}{2}, x = - \frac{7}{2}

Löse

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

Die Lösungen sind

x = \frac{7}{2}, x = - \frac{7}{2}, x = \frac{1}{2} i, x = - \frac{1}{2} i

Graph

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