Докажите неравенство: a(a-10)>4*(a-13).

\[a(a - 10) > 4 \cdot (a - 13)\]

\[a^{2} - 10a - 4a + 52 > 0\]

\[a^{2} - 14a + 52 > 0\]

\[a^{2} - 14a + 49 + 3 > 0\]

\[(a - 7)^{2} + 3 > 0\]

\[(a - 7)^{2} \geq 0;\ \ 3 > 0 \Longrightarrow верно.\]