3^3=2^3(c^3)

Lösung

3^{3} = 2^{3} (c^{3})

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

Schritte zur Lösung

3^{3} = 2^{3} (c^{3})

Tausche die Seiten

2^{3} (c^{3}) = 3^{3}

3^{3} = 27

2^{3} c^{3} = 27

Teile beide Seiten durch

8

c^{3} = \frac{27}{8}

Für

x^{3} = f (a)

sind die Lösungen

x = 3 f (a), 3 f (a) \frac{- 1 - 3 i}{2}, 3 f (a) \frac{- 1 + 3 i}{2}

c = 3 \frac{27}{8}, c = 3 \frac{27}{8} \frac{- 1 + 3 i}{2}, c = 3 \frac{27}{8} \frac{- 1 - 3 i}{2}

3 \frac{27}{8} = \frac{3}{2}

Vereinfache

3 \frac{27}{8} \frac{- 1 + 3 i}{2} : - \frac{3}{4} + \frac{3 3}{4} i

Vereinfache

3 \frac{27}{8} \frac{- 1 - 3 i}{2} : - \frac{3}{4} - \frac{3 3}{4} i

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

(4 x^{2} + 3 x - 10)^{2} = 9 x^{4}

35 x^{4} - 2 x^{2} - 1 = 0

x^{12} - 3 = 9

81 x^{3} - 192 = 0

x^{3} - 5 x^{2} + 2 x + 14 = x^{2} - 3 x + 2