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Beliebt Algebra >

x^8= 1/2

Lösung

x^{8} = \frac{1}{2}

Lösung

x = \frac{1}{4 2}, x = - \frac{1}{4 2}, x = - \frac{1}{4 2}, x = - - \frac{1}{4 2}, x = \frac{2 ^{\frac{3}{8}}}{2} + i \frac{2 ^{\frac{3}{8}}}{2}, x = - \frac{2 ^{\frac{3}{8}}}{2} - i \frac{2 ^{\frac{3}{8}}}{2}, x = \frac{2 ^{\frac{3}{8}}}{2} - i \frac{2 ^{\frac{3}{8}}}{2}, x = - \frac{2 ^{\frac{3}{8}}}{2} + i \frac{2 ^{\frac{3}{8}}}{2}

Schritte zur Lösung

x^{8} = \frac{1}{2}

Schreibe die Gleichung um mit

u = x^{2}

und

u^{4} = x^{8}

u^{4} = \frac{1}{2}

Löse

u^{4} = \frac{1}{2} : u = \frac{1}{2}, u = - \frac{1}{2}, u = - \frac{1}{2}, u = - - \frac{1}{2}

u = \frac{1}{2}, u = - \frac{1}{2}, u = - \frac{1}{2}, u = - - \frac{1}{2}

Setze

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

löse für

x

Löse

x^{2} = \frac{1}{2} : x = \frac{1}{4 2}, x = - \frac{1}{4 2}

Löse

x^{2} = - \frac{1}{2} : x = - \frac{1}{4 2}, x = - - \frac{1}{4 2}

Löse

x^{2} = - \frac{1}{2} : x = \frac{2 ^{\frac{3}{8}}}{2} + i \frac{2 ^{\frac{3}{8}}}{2}, x = - \frac{2 ^{\frac{3}{8}}}{2} - i \frac{2 ^{\frac{3}{8}}}{2}

Löse

x^{2} = - - \frac{1}{2} : x = \frac{2 ^{\frac{3}{8}}}{2} - i \frac{2 ^{\frac{3}{8}}}{2}, x = - \frac{2 ^{\frac{3}{8}}}{2} + i \frac{2 ^{\frac{3}{8}}}{2}

Die Lösungen sind

x = \frac{1}{4 2}, x = - \frac{1}{4 2}, x = - \frac{1}{4 2}, x = - - \frac{1}{4 2}, x = \frac{2 ^{\frac{3}{8}}}{2} + i \frac{2 ^{\frac{3}{8}}}{2}, x = - \frac{2 ^{\frac{3}{8}}}{2} - i \frac{2 ^{\frac{3}{8}}}{2}, x = \frac{2 ^{\frac{3}{8}}}{2} - i \frac{2 ^{\frac{3}{8}}}{2}, x = - \frac{2 ^{\frac{3}{8}}}{2} + i \frac{2 ^{\frac{3}{8}}}{2}

Graph

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