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