SOLUTION: the sum of a number and its reciprocal is 10/3 what is the number?

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Question 48155: the sum of a number and its reciprocal is 10/3 what is the number?
Found 2 solutions by cowess, Earlsdon:
Answer by cowess(34) About Me  (Show Source):
You can put this solution on YOUR website!
say the number is x
x+%2B+1%2Fx+=+10%2F3
3x%5E2+%2B+3+=+10x
%283x-1%29%28x-3%29=0
x=%281%2F3%29or3

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let n be the required number.
n%2B%281%2Fn%29+=+10%2F3 Simplift this.
%28n%5E2%2B1%29%2Fn+=+10%2F3 Multiply both sides by n.
n%5E2%2B1+=+10n%2F3 Multiply both sides by 3.
3n%5E2%2B3+=+10n Subtract 10n from both sides.
3n%5E2-10n%2B3+=+0 Solve this quadratic equation by factoring.
3n%5E2-10n%2B3+=+%283n-1%29%28n-3%29 Apply the zero products principle.
3n-1+=+0 and/or n-3+=+0
If 3n-1+=+0 then 3n+=+1 and n+=+1%2F3
If n-3+=+0 then n+=+3
The answer is there are two numbers that meet the given criteria:
1%2F3 and 3