Reference: Nordic Mathematical Contest, 1987-2009, R. Todev.
Let a, b, and c be real numbers different from 0 and . Prove that inequality
holds. When does the equality hold?
We know that a, b and c are real, distinct and also non-zero and also that .
Hence, , we have , or
On simplifying this, we immediately have
A sufficient condition for equality is . If , then . which makes the proved inequality a strict one. So, is a necessary condition for equality too.