SOLUTION: The sum of a number and its reciprocal is 10/3. What is the number? I think the formula should be x + 1/x = 10/3. Is that correct? How do I solve? Thank you in advance for yo

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Question 413914: The sum of a number and its reciprocal is 10/3. What is the number?
I think the formula should be x + 1/x = 10/3. Is that correct? How do I solve?
Thank you in advance for your help!
cheers!

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!

Hi
Let x represent the number
Question states***
x + 1/x = 10/3 |good work
Solving for x
3x^2 + 3 = 10x
3x^2 - 10x + 3 = 0
factoring
(3x -1)(x - 3) = 0 Note:SUM of the inner product(-x) and the outer product(-3x) = -10x
(3x -1)=0 x = 1/3
(x - 3) = 0 x = 3
CHECKING our Answer(s)***
1/3 + 3 = 10/3
3 + 1/3 = 10/3