SOLUTION: The sum of a number and it's reciprocal is 10/3. What is the number ?

Question 320138: The sum of a number and it's reciprocal is 10/3. What is the number ?
Answer by CharlesG2(834) (Show Source): You can put this solution on YOUR website!
The sum of a number and it's reciprocal is 10/3. What is the number ?
let x = the number
let 1/x = the reciprocal of the number
x + 1/x = 10/3
x^2 + 1 = (10/3)x (multiplied both sides by x)
x^2 - (10/3)x = -1
x^2 - (10/3)x + (-5/3)^2 = -1 + (-5/3)^2 (completed the square)
(x - 5/3)(x - 5/3) = x^2 - (5/3)x - (5/3)x + (-5/3)^2 (by use of FOIL)
(x - 5/3)^2 = -1 + 25/9 = -9/9 + 25/9 = 16/9
x - 5/3 = 4/3
x = 9/3 = 3
its reciprocal 1/x = 1/3

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