Given $3abc=2(a+b+c)$ Prove that $8(ab+bc+ca) \leq 5a^2b^2c^2+8 \leq 5(a^2+b^2+c^2)+18$ How to procees Can anyone give any hints
2026-03-30 04:37:49.1774845469
Prove the inequality with simple concepts
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After homogenization the both inequalities are equivalent to $\sum\limits_{cyc}(5a^3-3a^2b-3a^2c+abc)\geq0$, which is obvious.