What is the answer to x^{-6}-7x^{-3}-8=0 ?

The answer to x^{-6}-7x^{-3}-8=0 is

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x^{-6}-7x^{-3}-8=0

x^{- 6} - 7 x^{- 3} - 8 = 0

x = - 1, x = \frac{1}{2} - \frac{3}{2} i, x = \frac{1}{2} + \frac{3}{2} i, x = \frac{1}{2}, x = - \frac{1}{4} + \frac{3}{4} i, x = - \frac{1}{4} - \frac{3}{4} i

Solution steps

x^{- 6} - 7 x^{- 3} - 8 = 0

Refine

\frac{1}{x ^{6}} - \frac{7}{x ^{3}} - 8 = 0

Multiply by LCM

1 - 7 x^{3} - 8 x^{6} = 0

Solve

1 - 7 x^{3} - 8 x^{6} = 0 : x = - 1, x = \frac{1}{2} - \frac{3}{2} i, x = \frac{1}{2} + \frac{3}{2} i, x = \frac{1}{2}, x = - \frac{1}{4} + \frac{3}{4} i, x = - \frac{1}{4} - \frac{3}{4} i

x = - 1, x = \frac{1}{2} - \frac{3}{2} i, x = \frac{1}{2} + \frac{3}{2} i, x = \frac{1}{2}, x = - \frac{1}{4} + \frac{3}{4} i, x = - \frac{1}{4} - \frac{3}{4} i

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

x = - 1, x = \frac{1}{2} - \frac{3}{2} i, x = \frac{1}{2} + \frac{3}{2} i, x = \frac{1}{2}, x = - \frac{1}{4} + \frac{3}{4} i, x = - \frac{1}{4} - \frac{3}{4} i

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

\frac{40}{x} = \frac{2}{1}

\frac{x}{x - 3} + 1 = \frac{7}{x - 3}

n (x) = \frac{( 7 x + 5 )}{( x - 9 )}

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