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# algebra

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The difference between a number and its reciprocal is 3. What are the possible values of the number?

Jul 21, 2022

#1
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We have the equation: $$x - {1 \over x} = 3$$

Solve as follows:

$${x^2 \over x} - {1 \over x} = 3$$

$${x^2 - 1 \over x} = 3$$

$$x^2 - 1 = 3x$$

$$x^2 - 3x - 1 = 0$$

Jul 21, 2022
#2
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$$x - \frac{1}{x} = 3$$

$$x^2 - 1 = 3x$$

$$x^2 - 3x -1 = 0$$

$$x = \frac{3\pm\sqrt{13}}{2}$$

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Jul 21, 2022