SOLUTION: The sum of a number and its reciprocal is 10/3. What is the number? Thank you for anyone that can help! I just know I'm setting it up all wrong somehow. :/

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Question 7718: The sum of a number and its reciprocal is 10/3. What is the number?
Thank you for anyone that can help!
I just know I'm setting it up all wrong somehow. :/
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let n be the unknown number, then:
n+%2B+1%2Fn+=+10%2F3 Multiply both sides by n.
n%5E2+%2B+1+=+10n%2F3 Multiply both sides by 3.
3n%5E2+%2B+3+=+10n Subtract 10n from both sides.
3n%5E2+-+10n+%2B+3+=+0 Solve this quadratic equation by factoring.
%283n+-+1%29%28n+-+3%29+=+0 Apply the zero product principle.
If 3n+-+1+=+0, then 3n+=+1, and n+=+1%2F3 or
If n+-+3+=+0, then n+=+3
The two numbers are: 3 and 1/3
Check:
3 + 1/3 = 9/3 + 1/3 = 10/3
1/3 + 3/1 = 1/3 + 9/3 = 10/3