SOLUTION: The sum of 2 times a number and twice its reciprocal is 20/3. Find the number(s).

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Question 945389: The sum of 2 times a number and twice its reciprocal is 20/3.
Find the number(s).
Answer by Horlaye(27) About Me  (Show Source):
You can put this solution on YOUR website!
Let x represent the number
From the sentence
2(x) + 2(1/x) = 20/3
2x + 2/x = 20/3
multiply both sides of the equation by 3x
6x^² + 6 = 20x
6x^² - 20x + 6 = 0
6x^² - 18x - 2x + 6 = 0
6x(x-3) -2(x-3) = 0
(6x-2) (x-3) = 0
6x-2 = 0 or x-3 = 0
6x = 2 or. x = 3
x = 2/6
x = 1/3
Since x represented the number
Therefore x = 1/3 or 3