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Beliebt Algebra >

64j^6-27j^3=0

Lösung

64 j^{6} - 27 j^{3} = 0

Lösung

j = 3 \frac{27}{64}, j = 3 \frac{27}{64} \frac{- 1 + 3 i}{2}, j = 3 \frac{27}{64} \frac{- 1 - 3 i}{2}, j = 0

Schritte zur Lösung

64 j^{6} - 27 j^{3} = 0

Schreibe die Gleichung um mit

u = j^{3}

und

u^{2} = j^{6}

64 u^{2} - 27 u = 0

Löse

64 u^{2} - 27 u = 0 : u = \frac{27}{64}, u = 0

u = \frac{27}{64}, u = 0

Setze

u = j^{3} w i e d er e in,

löse für

j

Löse

j^{3} = \frac{27}{64} : j = 3 \frac{27}{64}, j = 3 \frac{27}{64} \frac{- 1 + 3 i}{2}, j = 3 \frac{27}{64} \frac{- 1 - 3 i}{2}

Löse

j^{3} = 0 : j = 0

Die Lösungen sind

j = 3 \frac{27}{64}, j = 3 \frac{27}{64} \frac{- 1 + 3 i}{2}, j = 3 \frac{27}{64} \frac{- 1 - 3 i}{2}, j = 0

Graph

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