Solve the equation: $x^{- 2} - 2 x^{- 1} = 8$

\frac{3}{4}, \frac{- 1}{2}

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\frac{1}{4}, \frac{- 1}{3}

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\frac{1}{3}, \frac{- 1}{2}

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

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Solution

The correct option is C $\frac{1}{4}, \frac{- 1}{2}$
Given, $x^{- 2} - 2 x^{- 1} = 8$
$\Rightarrow \frac{1}{x^{2}} - \frac{2}{x} = 8$
$\Rightarrow \frac{1 - 2 x}{x^{2}} = 8$
$\Rightarrow 1 - 2 x = 8 x^{2}$
$\Rightarrow 8 x^{2} + 2 x - 1 = 0$
$\Rightarrow (2 x + 1) (4 x - 1)$
$\Rightarrow x = \frac{1}{4}, \frac{- 1}{2}$

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