\(\Leftrightarrow4a^2-12ab-12ac-12bc+12b^2+12c^2>0\)
\(\Leftrightarrow3\left(a^2+4b^2+4c^2-4ab-4ac+8bc\right)+a^2-36bc>0\)
\(\Leftrightarrow3\left(a-2b-2c\right)^2+\frac{a^3-36abc}{a}>0\)
\(\Leftrightarrow3\left(a-2b-2c\right)^2+\frac{a^3-36}{a}>0\) ( luôn đúng do \(a^3>36\) )
Do đó ta có đpcm