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Beliebt Algebra >

a^4+a^2+4=0

Lösung

a^{4} + a^{2} + 4 = 0

Lösung

a = \frac{3}{2} + \frac{5}{2} i, a = - \frac{3}{2} - \frac{5}{2} i, a = \frac{3}{2} - \frac{5}{2} i, a = - \frac{3}{2} + \frac{5}{2} i

Schritte zur Lösung

a^{4} + a^{2} + 4 = 0

Schreibe die Gleichung um mit

u = a^{2}

und

u^{2} = a^{4}

u^{2} + u + 4 = 0

Löse

u^{2} + u + 4 = 0 : u = - \frac{1}{2} + i \frac{15}{2}, u = - \frac{1}{2} - i \frac{15}{2}

u = - \frac{1}{2} + i \frac{15}{2}, u = - \frac{1}{2} - i \frac{15}{2}

Setze

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

löse für

a

Löse

a^{2} = - \frac{1}{2} + i \frac{15}{2} : a = \frac{3}{2} + \frac{5}{2} i, a = - \frac{3}{2} - \frac{5}{2} i

Löse

a^{2} = - \frac{1}{2} - i \frac{15}{2} : a = \frac{3}{2} - \frac{5}{2} i, a = - \frac{3}{2} + \frac{5}{2} i

Die Lösungen sind

a = \frac{3}{2} + \frac{5}{2} i, a = - \frac{3}{2} - \frac{5}{2} i, a = \frac{3}{2} - \frac{5}{2} i, a = - \frac{3}{2} + \frac{5}{2} i

Graph

Beliebte Beispiele

y^{7} + y^{2} - 8 = 0

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0 = 12 x^{3} - 48 x^{2} + 36 x

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x^{4} + 8 x^{3} + 14 x^{2} - 2 x + 1 = 0

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