# Can someone help me figure this problem?

Find the sum of the reciprocals of two real numbers, given that these numbers have a sum of 75 and a product of 25.

I just need the process (i don't really need the answer), so i will actually learn. Thanks

I just need the process (i don't really need the answer), so i will actually learn. Thanks

active| newest | oldesta+b = 75, a*b=25, and s = (1/a) + (1/b)

That's the first step. The second step is

seeing patterns, or maybe you could call itremembering things you've seen before. In this case the trick is that (1/a) and (1/b) have a common denominator, which is a*b.s = (1/a) + (1/b) = b/(a*b) + a/(a*b) = (a+b)/(a*b)

So if you get that far, then you can do a couple of substitutions, namely:

a+b = 75 and a*b=25

s = (a+b)/(a*b) = 75/25 =3

Anyway, I know aelias36 already linked to Mr. Trinh's solution, which included this,and included the sort of brute force way of doing things, namely solving for a and b via the quadratic equation, and then substituting a and b into s = (1/a) + (1/b).

Your keywords included the word "challenge", which says to me that this is a problem in some sort of

competitivemath event, and for events like that, the math problems often come with built in short cuts, that the writers of the problems are probablyexpectingyou to use. So there alwaysmight bea trick, and it's not unreasonable to sort of look at the problem asking yourself, "Well, is there a trick to this? Is there a shortcut?"Anyway, I hope that gives you some insight into the "process" . A lot of it is about seeing patterns, and remembering stuff you've seen before.

I learned something about simple

A