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Beliebt Algebra >

256/625 =100r^6

Lösung

\frac{256}{625} = 100 r^{6}

Lösung

r = \frac{2}{5}, r = - \frac{2}{5}, r = \frac{1}{5} + \frac{3}{5} i, r = - \frac{1}{5} - \frac{3}{5} i, r = \frac{1}{5} - \frac{3}{5} i, r = - \frac{1}{5} + \frac{3}{5} i

Schritte zur Lösung

\frac{256}{625} = 100 r^{6}

Tausche die Seiten

100 r^{6} = \frac{256}{625}

Teile beide Seiten durch

100

r^{6} = \frac{64}{15625}

Schreibe die Gleichung um mit

u = r^{2}

und

u^{3} = r^{6}

u^{3} = \frac{64}{15625}

Löse

u^{3} = \frac{64}{15625} : u = 3 \frac{64}{15625}, u = 3 \frac{64}{15625} \frac{- 1 + 3 i}{2}, u = 3 \frac{64}{15625} \frac{- 1 - 3 i}{2}

u = 3 \frac{64}{15625}, u = 3 \frac{64}{15625} \frac{- 1 + 3 i}{2}, u = 3 \frac{64}{15625} \frac{- 1 - 3 i}{2}

Setze

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

löse für

r

Löse

r^{2} = 3 \frac{64}{15625} : r = \frac{2}{5}, r = - \frac{2}{5}

Löse

r^{2} = 3 \frac{64}{15625} \frac{- 1 + 3 i}{2} : r = \frac{1}{5} + \frac{3}{5} i, r = - \frac{1}{5} - \frac{3}{5} i

Löse

r^{2} = 3 \frac{64}{15625} \frac{- 1 - 3 i}{2} : r = \frac{1}{5} - \frac{3}{5} i, r = - \frac{1}{5} + \frac{3}{5} i

Die Lösungen sind

r = \frac{2}{5}, r = - \frac{2}{5}, r = \frac{1}{5} + \frac{3}{5} i, r = - \frac{1}{5} - \frac{3}{5} i, r = \frac{1}{5} - \frac{3}{5} i, r = - \frac{1}{5} + \frac{3}{5} i

Graph

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