m^4+m^2+1=0

Lösung

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

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

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

Schreibe die Gleichung um mit

u = m^{2}

und

u^{2} = m^{4}

u^{2} + u + 1 = 0

Löse

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

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}{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}{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

so l v e f or a, a^{3} - b^{3} = 0

(2 x^{2} - 7 x)^{2} + 2 x^{2} - 7 x = 20

(x)^{3} + (3 x)^{2} - x - 3 = 0

(x^{2} + x + 1)^{2} = x^{4} + 8 x^{2} + 1

x^{3} + x^{3} = 2