The sum of a number and its reciprocal is 65 28 . find the number.

Let
x--------> the number

we know that
x+(1/x)=65/28---------> x+1/x=65/28-----> multiply by x
x²+1=65/28*x-----> x²-(65/28)*x+1=0

using a graph tool----> to resolve the second order equation
see the attached figure
the solution is
x=1.75-----> 1 3/4----> (4*1+3)//4----> 7/4
so
7/4+4/7----> (7*7+4*4)/28----> (49+16)/28----> 65/28----> is correct

the answer is
the number is 7/4

To solve this problem you must apply the proccedure shown below:
 You have  that the sum of a number a its reciprocal is 68/28. Therefore, you have:

 x: the number.
 1/x: its reciprocal.

 x+(1/x)=65/28

 When you simplify the equation, you obtain:

 x^2-(65x/28)+1=0

 Solving the quadratic equation, you have:

 x=4/7; x=7/4

 Therefore, the answer is: 4/7 or 7/4.