SOLUTION: The sum of a number and its reciprocal is 10/3. What is the number?

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Question 312269: The sum of a number and its reciprocal is 10/3. What is the number?
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
let the number be x
reciprocal = 1/x
.
x+1/x = 10/3
x^2+1 / x =10/3
3(x^2+1)=10x
3x^2+3 = 10x
3x^2 -10x+3=0
3x^2-9x-x+3=0
3x(x-3)-1(x-3)=0
(3x-1)(x-3)=0
x=3 the number
CHECK
3 + 1/3 = 10/3