Let $a, b, c$ be positive real numbers. Show that $$a^5+b^5+c^5 \geq 5abc(b^2-ac)$$and determine when the equality occurs.
Source: 2022 Brazil Ibero TST P1
Tags: inequalities, Golden Ratio
Let $a, b, c$ be positive real numbers. Show that $$a^5+b^5+c^5 \geq 5abc(b^2-ac)$$and determine when the equality occurs.