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Beliebt Algebra >

4x^4+2x^2+1=0

Lösung

4 x^{4} + 2 x^{2} + 1 = 0

Lösung

x = \frac{1}{2 2} + \frac{3}{2 2} i, x = - \frac{1}{2 2} - \frac{3}{2 2} i, x = \frac{1}{2 2} - \frac{3}{4} 2 i, x = - \frac{1}{2 2} + \frac{3}{4} 2 i

Schritte zur Lösung

4 x^{4} + 2 x^{2} + 1 = 0

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

4 u^{2} + 2 u + 1 = 0

Löse

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

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

Setze

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

löse für

x

Löse

x^{2} = - \frac{1}{4} + i \frac{3}{4} : x = \frac{1}{2 2} + \frac{3}{2 2} i, x = - \frac{1}{2 2} - \frac{3}{2 2} i

Löse

x^{2} = - \frac{1}{4} - i \frac{3}{4} : x = \frac{1}{2 2} - \frac{3}{4} 2 i, x = - \frac{1}{2 2} + \frac{3}{4} 2 i

Die Lösungen sind

x = \frac{1}{2 2} + \frac{3}{2 2} i, x = - \frac{1}{2 2} - \frac{3}{2 2} i, x = \frac{1}{2 2} - \frac{3}{4} 2 i, x = - \frac{1}{2 2} + \frac{3}{4} 2 i

Graph

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