SOLUTION: Idk how to solve and check this problem, The sum of a number and its reciprocal is 10/3. What is the number?

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Question 15883: Idk how to solve and check this problem,
The sum of a number and its reciprocal is 10/3. What is the number?
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
Let the number =x
its reciprocal is 1/x
sum of the two numbers is = x+(1/x) = 10/3
(x^2+1)/x = 10/3
3*(x^2+1)=10*x
3x^2-10x+3 = 0...find 2 factors of 3*3=9 whose sum is -10 ... like -9 and -1
3x^2 -9x-x+3=0
3x*(x-3)-1*(x-3) =0
(3x-1)(x-3)=0
hence 3x-1 = 0 OR x-3 =0
3x=1 OR x=3
x=1/3 OR x=3