Questions on Word Problems: Numbers, consecutive odd/even, digits answered by real tutors!

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Question 143775: The sum of a number and its reciprocal is 13/6. What are the numbers?
Any help with this will be greatly appreciated.: The sum of a number and its reciprocal is 13/6. What are the numbers?
Any help with this will be greatly appreciated.
Answer by ptaylor(1170) About Me  (Show Source):
You can put this solution on YOUR website!

Let x=the number
Then 1/x= the reciprocal of the number
x+1/x=13/6 multiply each term by 6x
6x^2+6=13x subtract 13x from each side
6x^2-13x+6=0------------------quadratic in standard form. Solve using the quadratic formula:
x = (-b +- sqrt( b^2-4*a*c ))/(2*a)
x = (13 +- sqrt( 13^2-4*6*6 ))/(2*6)
x = (13 +- sqrt( 169-144))/(12)
x = (13 +- sqrt(25))/(12)
x = (13 +-5)/(12)
x = (13-5)/(12)=8/12=2/3 and
x = (13 +5)/(12)=18/12 =3/2
This tells us that the number can either be 2/3 or 3/2
CK
2/3+3/2=13/6
4/6+9/6=13/6
13/6=13/6
Hope this helps----ptaylor