In Search of a Magic Number

RAY: This next puzzler is mathematical in nature. Imagine two numbers, such that their product is equal to their sum. I'll give you two numbers: 5 and 1 and 1/4. You add them, and you get 6 and 1/4. You multiply them, and you also get 6 and 1/4.

TOM: You do?

RAY: You do! Now, I'm going to put on one additional condition. Both numbers have to be the same. For example, let's take 3/7ths as the number. 3/7ths and 3/7ths add up to 6/7. But, unfortunately, they multiply to 9/49ths. But if it worked, then, well, that would be the kind of answer I'm looking for.

TOM: So you're looking for whole numbers as well as fractions?

RAY: Any number you can think of. Fractions, irrational numbers, you name it, we'll use it.

Is there such a number that if you multiply it by itself the product is equal to adding it to itself?

If so, what are those numbers?

Of course zeros are not allowed, because everybody knows zero plus zero is equal to zero times zero. Zero is disqualified.

Think you know? Drop Ray a note!

[ Car Talk Puzzler ]