Докажите неравенство (x+3)(x-10)<(x-5)(x-2).

\[(x + 3)(x - 10) < (x - 5)(x - 2)\]

\[x^{2} - 10x + 3x - 30 < x^{2} - 2x - 5x + 20\]

\[x^{2} - 10x + 3x - x^{2} + 2x + 5x < 40\]

\[0 < 40 \Longrightarrow верно.\]