4x^3=92

Lösung

4 x^{3} = 92

x = 323, x = - 323 \frac{1}{2} + 323 \frac{3}{2} i, x = - 323 \frac{1}{2} - 323 \frac{3}{2} i

Schritte zur Lösung

4 x^{3} = 92

Teile beide Seiten durch

4

x^{3} = 23

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}

x = 323, x = 323 \frac{- 1 + 3 i}{2}, x = 323 \frac{- 1 - 3 i}{2}

Vereinfache

323 \frac{- 1 + 3 i}{2} : - 323 \frac{1}{2} + 323 \frac{3}{2} i

Vereinfache

323 \frac{- 1 - 3 i}{2} : - 323 \frac{1}{2} - 323 \frac{3}{2} i

x = 323, x = - 323 \frac{1}{2} + 323 \frac{3}{2} i, x = - 323 \frac{1}{2} - 323 \frac{3}{2} i

(12 s^{2} + 1)^{2} = 0

(x + 3)^{3} = 343

x^{3} + 5 x^{2} + 6 x + 0 = 0

3 x^{3} - 16 x^{2} + 23 x - 6 = 0

so l v e f or x, 4 x^{3} - 8 x^{2} - x + 2 = 0