algebra

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

Guest Jul 21, 2022

BuilderBoi · Answer 1 · 2022-07-21T02:00:01

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

Solve as follows:

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

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

$x^2 - 1 = 3x$

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

Now, just solve the quadratic...

nao173 · Answer 2 · 2022-07-21T03:16:04

$x - \frac{1}{x} = 3$

$x^2 - 1 = 3x$

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

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

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