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Beliebt Algebra >

6=-w^8

Lösung

6 = - w^{8}

Lösung

w = \frac{4 \frac{3}{2}}{2 \cdot 2 ^{\frac{3}{4}} 4 3 - 4 24} + \frac{2 \cdot 2 ^{\frac{3}{4}} 4 3 - 4 24}{2} i, w = - \frac{4 \frac{3}{2}}{2 \cdot 2 ^{\frac{3}{4}} 4 3 - 4 24} - \frac{2 \cdot 2 ^{\frac{3}{4}} 4 3 - 4 24}{2} i, w = - \frac{4 \frac{3}{2}}{4 24 + 2 \cdot 2 ^{\frac{3}{4}} 4 3} + \frac{4 24 + 2 \cdot 2 ^{\frac{3}{4}} 4 3}{2} i, w = \frac{4 \frac{3}{2}}{4 24 + 2 \cdot 2 ^{\frac{3}{4}} 4 3} - \frac{4 24 + 2 \cdot 2 ^{\frac{3}{4}} 4 3}{2} i, w = \frac{4 \frac{3}{2}}{4 24 + 2 \cdot 2 ^{\frac{3}{4}} 4 3} + \frac{4 24 + 2 \cdot 2 ^{\frac{3}{4}} 4 3}{2} i, w = - \frac{4 \frac{3}{2}}{4 24 + 2 \cdot 2 ^{\frac{3}{4}} 4 3} - \frac{4 24 + 2 \cdot 2 ^{\frac{3}{4}} 4 3}{2} i, w = - \frac{4 \frac{3}{2}}{2 \cdot 2 ^{\frac{3}{4}} 4 3 - 4 24} + \frac{2 \cdot 2 ^{\frac{3}{4}} 4 3 - 4 24}{2} i, w = \frac{4 \frac{3}{2}}{2 \cdot 2 ^{\frac{3}{4}} 4 3 - 4 24} - \frac{2 \cdot 2 ^{\frac{3}{4}} 4 3 - 4 24}{2} i

Schritte zur Lösung

6 = - w^{8}

Tausche die Seiten

- w^{8} = 6

Teile beide Seiten durch

- 1

w^{8} = - 6

Schreibe die Gleichung um mit

u = w^{2}

und

u^{4} = w^{8}

u^{4} = - 6

Löse

u^{4} = - 6 : u = 4 \frac{3}{2} + 4 \frac{3}{2} i, u = - 4 \frac{3}{2} - 4 \frac{3}{2} i, u = - 4 \frac{3}{2} + 4 \frac{3}{2} i, u = 4 \frac{3}{2} - 4 \frac{3}{2} i

u = 4 \frac{3}{2} + 4 \frac{3}{2} i, u = - 4 \frac{3}{2} - 4 \frac{3}{2} i, u = - 4 \frac{3}{2} + 4 \frac{3}{2} i, u = 4 \frac{3}{2} - 4 \frac{3}{2} i

Setze

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

löse für

w

Löse

w^{2} = 4 \frac{3}{2} + 4 \frac{3}{2} i : w = \frac{4 \frac{3}{2}}{2 \cdot 2 ^{\frac{3}{4}} 4 3 - 4 24} + \frac{2 \cdot 2 ^{\frac{3}{4}} 4 3 - 4 24}{2} i, w = - \frac{4 \frac{3}{2}}{2 \cdot 2 ^{\frac{3}{4}} 4 3 - 4 24} - \frac{2 \cdot 2 ^{\frac{3}{4}} 4 3 - 4 24}{2} i

Löse

w^{2} = - 4 \frac{3}{2} - 4 \frac{3}{2} i : w = - \frac{4 \frac{3}{2}}{4 24 + 2 \cdot 2 ^{\frac{3}{4}} 4 3} + \frac{4 24 + 2 \cdot 2 ^{\frac{3}{4}} 4 3}{2} i, w = \frac{4 \frac{3}{2}}{4 24 + 2 \cdot 2 ^{\frac{3}{4}} 4 3} - \frac{4 24 + 2 \cdot 2 ^{\frac{3}{4}} 4 3}{2} i

Löse

w^{2} = - 4 \frac{3}{2} + 4 \frac{3}{2} i : w = \frac{4 \frac{3}{2}}{4 24 + 2 \cdot 2 ^{\frac{3}{4}} 4 3} + \frac{4 24 + 2 \cdot 2 ^{\frac{3}{4}} 4 3}{2} i, w = - \frac{4 \frac{3}{2}}{4 24 + 2 \cdot 2 ^{\frac{3}{4}} 4 3} - \frac{4 24 + 2 \cdot 2 ^{\frac{3}{4}} 4 3}{2} i

Löse

w^{2} = 4 \frac{3}{2} - 4 \frac{3}{2} i : w = - \frac{4 \frac{3}{2}}{2 \cdot 2 ^{\frac{3}{4}} 4 3 - 4 24} + \frac{2 \cdot 2 ^{\frac{3}{4}} 4 3 - 4 24}{2} i, w = \frac{4 \frac{3}{2}}{2 \cdot 2 ^{\frac{3}{4}} 4 3 - 4 24} - \frac{2 \cdot 2 ^{\frac{3}{4}} 4 3 - 4 24}{2} i

Die Lösungen sind

w = \frac{4 \frac{3}{2}}{2 \cdot 2 ^{\frac{3}{4}} 4 3 - 4 24} + \frac{2 \cdot 2 ^{\frac{3}{4}} 4 3 - 4 24}{2} i, w = - \frac{4 \frac{3}{2}}{2 \cdot 2 ^{\frac{3}{4}} 4 3 - 4 24} - \frac{2 \cdot 2 ^{\frac{3}{4}} 4 3 - 4 24}{2} i, w = - \frac{4 \frac{3}{2}}{4 24 + 2 \cdot 2 ^{\frac{3}{4}} 4 3} + \frac{4 24 + 2 \cdot 2 ^{\frac{3}{4}} 4 3}{2} i, w = \frac{4 \frac{3}{2}}{4 24 + 2 \cdot 2 ^{\frac{3}{4}} 4 3} - \frac{4 24 + 2 \cdot 2 ^{\frac{3}{4}} 4 3}{2} i, w = \frac{4 \frac{3}{2}}{4 24 + 2 \cdot 2 ^{\frac{3}{4}} 4 3} + \frac{4 24 + 2 \cdot 2 ^{\frac{3}{4}} 4 3}{2} i, w = - \frac{4 \frac{3}{2}}{4 24 + 2 \cdot 2 ^{\frac{3}{4}} 4 3} - \frac{4 24 + 2 \cdot 2 ^{\frac{3}{4}} 4 3}{2} i, w = - \frac{4 \frac{3}{2}}{2 \cdot 2 ^{\frac{3}{4}} 4 3 - 4 24} + \frac{2 \cdot 2 ^{\frac{3}{4}} 4 3 - 4 24}{2} i, w = \frac{4 \frac{3}{2}}{2 \cdot 2 ^{\frac{3}{4}} 4 3 - 4 24} - \frac{2 \cdot 2 ^{\frac{3}{4}} 4 3 - 4 24}{2} i

Graph

Beliebte Beispiele

x^3-4x^2-5x+20=0

x^{3} - 4 x^{2} - 5 x + 20 = 0

x^{4} - 21 x^{2} + 80 = 0

x^{3} + 5 x^{2} = - 6 x

solvefor x,x^3-2x^2-5x+6=0

so l v e f or x, x^{3} - 2 x^{2} - 5 x + 6 = 0

solvefor F,t=(F^3+G)a

so l v e f or F, t = (F^{3} + G) a