x^{-8}-17x^{-4}+16=0

Lösung

x^{- 8} - 17 x^{- 4} + 16 = 0

x = 1, x = - 1, x = i, x = - i, x = \frac{1}{2}, x = - \frac{1}{2}, x = \frac{1}{2} i, x = - \frac{1}{2} i

Schritte zur Lösung

x^{- 8} - 17 x^{- 4} + 16 = 0

Fasse zusammen

\frac{1}{x ^{8}} - \frac{17}{x ^{4}} + 16 = 0

Multipliziere mit dem kleinsten gemeinsamen Multiplikator

1 - 17 x^{4} + 16 x^{8} = 0

Löse

1 - 17 x^{4} + 16 x^{8} = 0 : x = 1, x = - 1, x = i, x = - i, x = \frac{1}{2}, x = - \frac{1}{2}, x = \frac{1}{2} i, x = - \frac{1}{2} i

x = 1, x = - 1, x = i, x = - i, x = \frac{1}{2}, x = - \frac{1}{2}, x = \frac{1}{2} i, x = - \frac{1}{2} i

Überprüfe die Lösungen

Bestimme unbestimmte (Singularitäts-)Punkte:

x = 0

Kombine die undefinierten Punkte mit den Lösungen:

x = 1, x = - 1, x = i, x = - i, x = \frac{1}{2}, x = - \frac{1}{2}, x = \frac{1}{2} i, x = - \frac{1}{2} i

\frac{2}{t + 6} = \frac{3}{t - 1}

x = \frac{a x + b}{c x + d}

6 - \frac{5}{x} = 4 + \frac{3}{x}

\frac{2}{x + 2} + 2 = \frac{8}{x + 2}

\frac{6 x ^{2} + 2 x - 4}{3 x + 1} = 2 x