The sum of a number and its reciprocal is 265 Find the numbe

The sum of a number and its reciprocal is 26/5. Find the number.

Let the no be x

Then its reciprocal be 1/x

now , as per Question sum of no and its reciprocal is 26/5

x + 1/x = 26/5

Muliplying both side by 5x we get ,

x * 5x + 1/x * 5x = 26/5 * 5x

5x^2 + 5 = 26x

5x^2 - 26x + 5 = 0

( x- 5) ( 5x-1 ) = 0

x= 5 or x = 1/5

so , this is the answer.