SOLUTION: How would I solve this? The sum of a number and its reciprocal is 10/3. What is the number?

Algebra ->  Functions -> SOLUTION: How would I solve this? The sum of a number and its reciprocal is 10/3. What is the number?      Log On


   

Question 458390: How would I solve this?
The sum of a number and its reciprocal is 10/3. What is the number?
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
x + 1/x = 10/3
3x^2+3=10x multiply each side by 3x.
3x^2-10x+3=0
3*3=9. Two factors of 9 whose sum is -10 are -9 and -1.
3x^2-9x-x+3=0
3x(x-3)-(x-3)=0
(3x-1)(x-3)=0
x=3, x=1/3
.
Ed