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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
avatar+2448 
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We have the equation: \(x - {1 \over x} = 3\)

 

Solve as follows: 

 

\({x^2 \over x} - {1 \over x} = 3\)

\({x^2 - 1 \over x} = 3\)

\(x^2 - 1 = 3x \) 

\(x^2 - 3x - 1 = 0\)

 

Now, just solve the quadratic...

 Jul 21, 2022
 #2
avatar+11 
0

\(x - \frac{1}{x} = 3\)

 

\(x^2 - 1 = 3x\)

 

\(x^2 - 3x -1 = 0\)

 

\(x = \frac{3\pm\sqrt{13}}{2}\)

 

 

smiley

.
 Jul 21, 2022

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