HELP! WILL MARK BRAINLIEST!! Suppose for two real numbers x and y, both the sum x+y and product xy are integers. Either prove x

Question

xeze [42]

4 years ago

10

HELP! WILL MARK BRAINLIEST!! Suppose for two real numbers x and y, both the sum x+y and product xy are integers. Either prove x

and y must be rational numbers, or find a counterexample.

Mathematics

1 answer:

klasskru [66] · Answer 1 · 2022-02-04T21:40:27+03:00

Step-by-step explanation:

A man by the name of Luigi Fonti wrote this. I hope it can guide you, as it did for me! "The set of rational numbers is closed for all the four operations, so x+y, x-y, x*y and x/y are rational too. And it is easy to demonstrate. A rational number can be expressed as a fraction of two integers. So, x can be expressed as a/b and y as c/d. Hence x+y = a/b + c/d = (ad+bc)/bd, which, as fraction of two integers, is rational."