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. :/

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) (Show Source): You can put this solution on YOUR website!
Let n be the unknown number, then:
Multiply both sides by n.
Multiply both sides by 3.
Subtract 10n from both sides.
Solve this quadratic equation by factoring.
Apply the zero product principle.
If , then , and or
If , then
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
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