Problem
For any $\triangle ABC$, let $a,b,c$ be the length of the side respectively. Show that $$(2b+2c-2a)^3(a+b+c)\geq18a^2bc.$$
2026-03-25 17:42:08.1774460528
Let $a,b,c$ be the length of the side $BC,CA,AB$ respectively for $\triangle ABC$. Show that $(2b+2c-2a)^3(a+b+c)\geq18a^2bc$.
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It's wrong. Try $b=c=3$ and $a=5$.