If the sum of two positive numbers is 65 and the square root of their product is 26, then the sum of their reciprocals is:

$$\eqalign{ & {\text{Lets first number}} = a \cr & {\text{Second number}} = b \cr & a + b = 65 \cr & \sqrt {a \times b} = 26 \cr & ab = 676 \cr & {\text{Sum of reciprocal}} = \frac{1}{a} + \frac{1}{b} \cr & = \frac{{b + a}}{{ab}} \cr & = \frac{{65}}{{676}} \cr & = \frac{5}{{52}} \cr} $$