SOLUTION: The sum of a number and its reciprocal is 34/15. Find the number.

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Question 198557: The sum of a number and its reciprocal is 34/15. Find the number.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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The sum of a number and its reciprocal is 34/15. Find the number.
:
x + 1%2Fx = 34%2F15
Multiply equation by 15x, results
15x(x) + 15(1) = 34x
:
Arrange as a quadratic equation
15x^2 - 34x + 15 = 0
Factors to:
(5x - 3)(3x - 5) = 0
Two solutions
5x = 3
x = 3%2F5
and
3x = 5
x = 5%2F3
;
;
Check solution using the 1st solution
3%2F5 + 5%2F3 =
9%2F15 + 25%2F15 = 34%2F15