Докажите неравенство: a(a-2)>6*(a-3).

\[a(a - 2) > 6 \cdot (a - 3)\]

\[a^{2} - 2a > 6a - 18\]

\[a^{2} - 8a + 18 > 0\]

\[a^{2} - 8a + 16 + 2 > 0\]

\[(a - 4)^{2} + 2 > 0\]

\[(a - 4)^{2} \geq 0;\ \ 2 > 0 \Longrightarrow верно.\]