SOLUTION: Use the five-step method to solve. Check your answer. The sum of a number and it's reciprocal is 10/3. What is the number?

Algebra ->  Algebra  -> Functions -> SOLUTION: Use the five-step method to solve. Check your answer. The sum of a number and it's reciprocal is 10/3. What is the number?      Log On

Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!
Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!

   

Question 54335: Use the five-step method to solve. Check your answer.
The sum of a number and it's reciprocal is 10/3. What is the number?
Answer by rchill(405) About Me  (Show Source):
You can put this solution on YOUR website!
I'm not familiar with the 5-step method, but the equation is x%2B1%2Fx=10%2F3, which becomes:
3x%2B3%2Fx=10 after multiplying both sides by 3
3x%5E2%2B3=10x after multiplying both sides by x
3x%5E2-10x%2B3=0 after subtracting 10x from both sides
%283x-1%29%28x-3%29=0 after factorization
So, either 3x-1=0 or x-3=0, which means that x can be either 1%2F3 or 3.