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Beliebt Algebra >

125/64 =125r^6

Lösung

\frac{125}{64} = 125 r^{6}

Lösung

r = \frac{1}{2}, r = - \frac{1}{2}, r = \frac{1}{4} + \frac{3}{4} i, r = - \frac{1}{4} - \frac{3}{4} i, r = \frac{1}{4} - \frac{3}{4} i, r = - \frac{1}{4} + \frac{3}{4} i

Schritte zur Lösung

\frac{125}{64} = 125 r^{6}

Tausche die Seiten

125 r^{6} = \frac{125}{64}

Teile beide Seiten durch

125

r^{6} = \frac{1}{64}

Schreibe die Gleichung um mit

u = r^{2}

und

u^{3} = r^{6}

u^{3} = \frac{1}{64}

Löse

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

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

Setze

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

löse für

r

Löse

r^{2} = 3 \frac{1}{64} : r = \frac{1}{2}, r = - \frac{1}{2}

Löse

r^{2} = 3 \frac{1}{64} \frac{- 1 + 3 i}{2} : r = \frac{1}{4} + \frac{3}{4} i, r = - \frac{1}{4} - \frac{3}{4} i

Löse

r^{2} = 3 \frac{1}{64} \frac{- 1 - 3 i}{2} : r = \frac{1}{4} - \frac{3}{4} i, r = - \frac{1}{4} + \frac{3}{4} i

Die Lösungen sind

r = \frac{1}{2}, r = - \frac{1}{2}, r = \frac{1}{4} + \frac{3}{4} i, r = - \frac{1}{4} - \frac{3}{4} i, r = \frac{1}{4} - \frac{3}{4} i, r = - \frac{1}{4} + \frac{3}{4} i

Graph

Beliebte Beispiele

x^{6} + 3 x^{3} - 7 = 0

x^{4} - 12 x^{2} = 0

x^{6} - 14 x^{3} + 40 = 0

solvefor x,x^3+y^3=6

so l v e f or x, x^{3} + y^{3} = 6

3 x^{5} - 5 x^{3} = 0