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) About Me  (Show Source):
You can put this solution on YOUR website!
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x + 1%2Fx = 8  ====> multiply both sides by x  ====>

x%5E2+%2B+1 = 8x  ====>  collect x-terms on the left side. Move the constant term to the right side  ====>

x%5E2+-+8x = -1  ====>  add 16 to both sides  ====>

x%5E2+-+2%2A4x+%2B+16 = -1 + 16  ====>  complete the square on the left side  ====>

%28x-4%29%5E2 = 15  ====>  take the saure root from both sides  ====>

x - 4 = +/- sqrt%2815%29.


Answer.  There are two solutions:   4+%2B+sqrt%2815%29  and  4-sqrt%2815%29.

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.