**Reference: Nordic Mathematical Contest, 1987-2009, R. Todev.**

**Question:**

Let a, b, and c be real numbers different from 0 and . Prove that inequality

holds. When does the equality hold?

Proof:

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.

-Nalin Pithwa.

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