MathDB

Prove that given three positive numbers, we can choose two of them, say

x

and

y,

with

x >y

such that

\frac{x-y}{1 +xy }<1.

Prove also that if the number

1

that appears in the second member of the previous inequality is replaced by a lower number, even if very close to

1

, the previous proposition is false.

Problem Statement