What is the answer to x^{-2}-2x^{-1}=8 ?

The answer to x^{-2}-2x^{-1}=8 is x= 1/4 ,x=-1/2

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x^{-2}-2x^{-1}=8

x^{- 2} - 2 x^{- 1} = 8

x = \frac{1}{4}, x = - \frac{1}{2}

Solution steps

x^{- 2} - 2 x^{- 1} = 8

Refine

\frac{1}{x ^{2}} - \frac{2}{x} = 8

Multiply by LCM

1 - 2 x = 8 x^{2}

Solve

1 - 2 x = 8 x^{2} : x = \frac{1}{4}, x = - \frac{1}{2}

x = \frac{1}{4}, x = - \frac{1}{2}

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

x = \frac{1}{4}, x = - \frac{1}{2}

\frac{x}{x - 14} = \frac{- 2}{x - 5}

45 = - \frac{1}{x} - 45

\frac{3}{y} = - 6

\frac{3 - z}{z - 4} = \frac{1}{2}

t, \frac{x - v t}{t} = c - v

What is the answer to x^{-2}-2x^{-1}=8 ?
The answer to x^{-2}-2x^{-1}=8 is x= 1/4 ,x=-1/2
Solve for x: x^{-2}-2x^{-1}=8
The solution is x= 1/4 ,x=-1/2