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Beliebt Algebra >

x^8-x^4-30=0

Lösung

x^{8} - x^{4} - 30 = 0

Lösung

x = 6, x = - 6, x = 6 i, x = - 6 i, x = \frac{4 5}{2} + \frac{4 5}{2} i, x = - \frac{4 5}{2} - \frac{4 5}{2} i, x = \frac{4 5}{2} - \frac{4 5}{2} i, x = - \frac{4 5}{2} + \frac{4 5}{2} i

Schritte zur Lösung

x^{8} - x^{4} - 30 = 0

Schreibe die Gleichung um mit

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

und

u^{4} = x^{8}

u^{4} - u^{2} - 30 = 0

Löse

u^{4} - u^{2} - 30 = 0 : u = 6, u = - 6, u = 5 i, u = - 5 i

u = 6, u = - 6, u = 5 i, u = - 5 i

Setze

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

löse für

x

Löse

x^{2} = 6 : x = 6, x = - 6

Löse

x^{2} = - 6 : x = 6 i, x = - 6 i

Löse

x^{2} = 5 i : x = \frac{4 5}{2} + \frac{4 5}{2} i, x = - \frac{4 5}{2} - \frac{4 5}{2} i

Löse

x^{2} = - 5 i : x = \frac{4 5}{2} - \frac{4 5}{2} i, x = - \frac{4 5}{2} + \frac{4 5}{2} i

Die Lösungen sind

x = 6, x = - 6, x = 6 i, x = - 6 i, x = \frac{4 5}{2} + \frac{4 5}{2} i, x = - \frac{4 5}{2} - \frac{4 5}{2} i, x = \frac{4 5}{2} - \frac{4 5}{2} i, x = - \frac{4 5}{2} + \frac{4 5}{2} i

Graph

Beliebte Beispiele

4x^3-x^2+100x-25=0

4 x^{3} - x^{2} + 100 x - 25 = 0

z^4+4z^3+2z^2-12z-15=0

z^{4} + 4 z^{3} + 2 z^{2} - 12 z - 15 = 0

3a^3-147a=-2a^2+98

3 a^{3} - 147 a = - 2 a^{2} + 98

695 = 5 x^{3}

z^{3} + 1 - i = 0