4x^{-6}+4x^{-3}-15=0

Lösung

4 x^{- 6} + 4 x^{- 3} - 15 = 0

x = - 3 \frac{2}{5}, x = \frac{5 ^{\frac{2}{3}} 3 2}{10} - i \frac{5 ^{\frac{2}{3}} 3 2 3}{10}, x = \frac{5 ^{\frac{2}{3}} 3 2}{10} + i \frac{5 ^{\frac{2}{3}} 3 2 3}{10}, x = 3 \frac{2}{3}, x = - 3 \frac{2}{3} \frac{1}{2} + 3 \frac{2}{3} \frac{3}{2} i, x = - 3 \frac{2}{3} \frac{1}{2} - 3 \frac{2}{3} \frac{3}{2} i

Schritte zur Lösung

4 x^{- 6} + 4 x^{- 3} - 15 = 0

Fasse zusammen

\frac{4}{x ^{6}} + \frac{4}{x ^{3}} - 15 = 0

Multipliziere mit dem kleinsten gemeinsamen Multiplikator

4 + 4 x^{3} - 15 x^{6} = 0

Löse

4 + 4 x^{3} - 15 x^{6} = 0 : x = - 3 \frac{2}{5}, x = \frac{5 ^{\frac{2}{3}} 3 2}{10} - i \frac{5 ^{\frac{2}{3}} 3 2 3}{10}, x = \frac{5 ^{\frac{2}{3}} 3 2}{10} + i \frac{5 ^{\frac{2}{3}} 3 2 3}{10}, x = 3 \frac{2}{3}, x = - 3 \frac{2}{3} \frac{1}{2} + 3 \frac{2}{3} \frac{3}{2} i, x = - 3 \frac{2}{3} \frac{1}{2} - 3 \frac{2}{3} \frac{3}{2} i

x = - 3 \frac{2}{5}, x = \frac{5 ^{\frac{2}{3}} 3 2}{10} - i \frac{5 ^{\frac{2}{3}} 3 2 3}{10}, x = \frac{5 ^{\frac{2}{3}} 3 2}{10} + i \frac{5 ^{\frac{2}{3}} 3 2 3}{10}, x = 3 \frac{2}{3}, x = - 3 \frac{2}{3} \frac{1}{2} + 3 \frac{2}{3} \frac{3}{2} i, x = - 3 \frac{2}{3} \frac{1}{2} - 3 \frac{2}{3} \frac{3}{2} i

Überprüfe die Lösungen

Bestimme unbestimmte (Singularitäts-)Punkte:

x = 0

Kombine die undefinierten Punkte mit den Lösungen:

x = - 3 \frac{2}{5}, x = \frac{5 ^{\frac{2}{3}} 3 2}{10} - i \frac{5 ^{\frac{2}{3}} 3 2 3}{10}, x = \frac{5 ^{\frac{2}{3}} 3 2}{10} + i \frac{5 ^{\frac{2}{3}} 3 2 3}{10}, x = 3 \frac{2}{3}, x = - 3 \frac{2}{3} \frac{1}{2} + 3 \frac{2}{3} \frac{3}{2} i, x = - 3 \frac{2}{3} \frac{1}{2} - 3 \frac{2}{3} \frac{3}{2} i

x + \frac{1}{x} + 4 = 0

\frac{5}{x + 5} = \frac{3}{x + 6}

\frac{1}{1 + 2 ( \frac{x}{4} )} = 0.5

\frac{8 x + 4}{4 - 2 x} = - 6

\frac{1}{x ^{2}} + 2 = \frac{1}{4}