SOLUTION: The sum of a number and its reciprocal is 13/6. What are the numbers? Any help with this will be greatly appreciated.

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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.
Answer by ptaylor(2198) 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+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%2813+%2B-+sqrt%28+13%5E2-4%2A6%2A6+%29%29%2F%282%2A6%29+
x+=+%2813+%2B-+sqrt%28+169-144%29%29%2F%2812%29+
x+=+%2813+%2B-+sqrt%2825%29%29%2F%2812%29+
x+=+%2813+%2B-5%29%2F%2812%29+
x+=+%2813-5%29%2F%2812%29=8%2F12=2%2F3+ and
x+=+%2813+%2B5%29%2F%2812%29=18%2F12+=3%2F2
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