anonymous
  • anonymous
The sum of an integer and its reciprocal is 65/8. Find the integer.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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dan815
  • dan815
|dw:1370684327523:dw|
anonymous
  • anonymous
$$x+\frac1x=\frac{65}8=\frac{64+1}8=8+\frac18\quad\implies x=8$$
anonymous
  • anonymous
@FutureMathProfessor not quite...

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Jack1
  • Jack1
... what about x = (1/8)...? doesnt that fit the equation?
anonymous
  • anonymous
@Jack1 \(1/8\) is not an integer.
Jack1
  • Jack1
ah, gotcha, didnt read the q, sorry
anonymous
  • anonymous
Is there any method to find the value of x, instead of substituting a value at random?
anonymous
  • anonymous
That wasn't substituting a value at random... but there's a more annoying way.$$x+\frac1x=\frac{65}8\\x^2+1=\frac{65}8x\\x^2-\frac{65}8x+1=0$$Can you solve?
radar
  • radar
|dw:1370692246929:dw|
radar
  • radar
|dw:1370694319534:dw|

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