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Beliebt Algebra >

64j^6-27j^9=0

Lösung

64 j^{6} - 27 j^{9} = 0

Lösung

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

Schritte zur Lösung

64 j^{6} - 27 j^{9} = 0

Schreibe in der Standard Form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

- 27 j^{9} + 64 j^{6} = 0

Schreibe die Gleichung um mit

u = j^{3}, u^{2} = j^{6}

und

u^{3} = j^{9}

- 27 u^{3} + 64 u^{2} = 0

Löse

- 27 u^{3} + 64 u^{2} = 0 : u = 0, u = \frac{64}{27}

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

Setze

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

löse für

j

Löse

j^{3} = 0 : j = 0

Löse

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

Die Lösungen sind

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

Graph

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