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Beliebt Algebra >

3m^6+4m^4+4m^2+1=0

Lösung

3 m^{6} + 4 m^{4} + 4 m^{2} + 1 = 0

Lösung

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

Schritte zur Lösung

3 m^{6} + 4 m^{4} + 4 m^{2} + 1 = 0

Schreibe die Gleichung um mit

u = m^{2}, u^{2} = m^{4}

und

u^{3} = m^{6}

3 u^{3} + 4 u^{2} + 4 u + 1 = 0

Löse

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

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

Setze

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

löse für

m

Löse

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

Löse

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

Löse

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

Die Lösungen sind

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

Graph

Beliebte Beispiele

x^{2} (4 x - 2) = 324

4x^3-72x^2+288x=0

4 x^{3} - 72 x^{2} + 288 x = 0

2 x^{3} - 3 x^{2} - 1 = 0

x^{3} - 1 = - x + 9

7 x^{6} - 42 x^{5} = 0