SOLUTION: Find a number such that the sum of the number at it's reciprocal is 8

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Question 1091925: Find a number such that the sum of the number at it's reciprocal is 8

Answer by ikleyn(52778)   (Show Source): You can put this solution on YOUR website!
.
 +  = 8  ====> multiply both sides by x  ====>

 = 8x  ====>  collect x-terms on the left side. Move the constant term to the right side  ====>

 = -1  ====>  add 16 to both sides  ====>

 = -1 + 16  ====>  complete the square on the left side  ====>

 = 15  ====>  take the saure root from both sides  ====>

x - 4 = +/- .


Answer.  There are two solutions:     and  .

Solved.

I applied the completing the square method to solve the quadratic equation.

To learn more about this method, see the leson
    - HOW TO solve quadratic equation by completing the square - Learning by examples
in this site.


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