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Beliebt Algebra >

x^4+x^2+25=0

Lösung

x^{4} + x^{2} + 25 = 0

Lösung

x = \frac{3}{2} + \frac{11}{2} i, x = - \frac{3}{2} - \frac{11}{2} i, x = \frac{3}{2} - \frac{11}{2} i, x = - \frac{3}{2} + \frac{11}{2} i

Schritte zur Lösung

x^{4} + x^{2} + 25 = 0

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

u^{2} + u + 25 = 0

Löse

u^{2} + u + 25 = 0 : u = - \frac{1}{2} + i \frac{3 11}{2}, u = - \frac{1}{2} - i \frac{3 11}{2}

u = - \frac{1}{2} + i \frac{3 11}{2}, u = - \frac{1}{2} - i \frac{3 11}{2}

Setze

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

löse für

x

Löse

x^{2} = - \frac{1}{2} + i \frac{3 11}{2} : x = \frac{3}{2} + \frac{11}{2} i, x = - \frac{3}{2} - \frac{11}{2} i

Löse

x^{2} = - \frac{1}{2} - i \frac{3 11}{2} : x = \frac{3}{2} - \frac{11}{2} i, x = - \frac{3}{2} + \frac{11}{2} i

Die Lösungen sind

x = \frac{3}{2} + \frac{11}{2} i, x = - \frac{3}{2} - \frac{11}{2} i, x = \frac{3}{2} - \frac{11}{2} i, x = - \frac{3}{2} + \frac{11}{2} i

Graph

Beliebte Beispiele

z^{6} = i

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21 x^{2} - 18 x - 3 x^{3} = 0

150x^2+0.38x^3-80=0

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x^3-12x^2+32x=0

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