The sum of a number and twice of its reciprocal is 51/7. Find the number

Question

The sum of a number and twice of its reciprocal is 51/7. Find the number

Answer 1

x + 2*(1/x) = 51/7

x + 2/x = 51/7

[x(7x)/7x] + [(7*2)/7x] = (51*x)/7x

7x^2 + 14 = 51x

7x^2 - 51x + 14 = 0

(x - 7) * (7x - 2) = 0

 

7x - 2 =0

7x=2

x = 2/7

 

x - 7 =0

x = 7

 

Since they are likely looking for an integer, the answer is 7.  To double check that:

 

(7) + 2(1/7) = 51/7

49/7 + 2/7 = 51/7

51/7 = 51/7