((x-1)/3)^3= 8/25

Lösung

(\frac{x - 1}{3})^{3} = \frac{8}{25}

x = \frac{6}{3 25} + 1, x = \frac{25 - 3 \cdot 2 5 ^{\frac{2}{3}}}{25} + i \frac{3 \cdot 2 5 ^{\frac{2}{3}} 3}{25}, x = \frac{25 - 3 \cdot 2 5 ^{\frac{2}{3}}}{25} - i \frac{3 \cdot 2 5 ^{\frac{2}{3}} 3}{25}

Schritte zur Lösung

(\frac{x - 1}{3})^{3} = \frac{8}{25}

Für

g^{3} (x) = f (a)

sind die Lösungen

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

Löse

\frac{x - 1}{3} = 3 \frac{8}{25} : x = \frac{6}{3 25} + 1

Löse

\frac{x - 1}{3} = 3 \frac{8}{25} \frac{- 1 + 3 i}{2} : x = \frac{25 - 3 \cdot 2 5 ^{\frac{2}{3}}}{25} + i \frac{3 \cdot 2 5 ^{\frac{2}{3}} 3}{25}

Löse

\frac{x - 1}{3} = 3 \frac{8}{25} \frac{- 1 - 3 i}{2} : x = \frac{25 - 3 \cdot 2 5 ^{\frac{2}{3}}}{25} - i \frac{3 \cdot 2 5 ^{\frac{2}{3}} 3}{25}

Die Lösungen sind

x = \frac{6}{3 25} + 1, x = \frac{25 - 3 \cdot 2 5 ^{\frac{2}{3}}}{25} + i \frac{3 \cdot 2 5 ^{\frac{2}{3}} 3}{25}, x = \frac{25 - 3 \cdot 2 5 ^{\frac{2}{3}}}{25} - i \frac{3 \cdot 2 5 ^{\frac{2}{3}} 3}{25}

x^{50} = 1

x^{4} - 2 x^{3} - 4 x + 5 = 0

\frac{x ^{4}}{3} = 16

\frac{5}{2} x + 1 - 2 \frac{x}{1} - 2 x = 1 - 2 \frac{( 3 - 2 x )}{4} x^{2} - 1

320 = \frac{x ^{7}}{2}