The sum of two numbers is 7 and their product is 25. Determine the sum of their reciprocals
Let the numbers be $\displaystyle x$ and $\displaystyle y$
you have
$\displaystyle x + y = 7$ ............(1)
$\displaystyle xy = 25$ ...............(2)
this is a system of simultaneous equations. you can solve for x and y (or just one of them, if you want), then you can find the value of the desired expression
$\displaystyle \frac 1x + \frac 1y = \cdots$