$\begin{array}{l}
y = {x^2} - 3x + 1\\
Voi\,{x_1},{x_2} \in \left( {2; + \infty } \right)\,ta\,co:\\
\frac{{f\left( {{x_1}} \right) - f\left( {{x_2}} \right)}}{{{x_1} - {x_2}}} = \frac{{x_1^2 - 3{x_1} + 1 - x_2^2 - 3{x_2} + 1}}{{{x_1} - {x_2}}}\\
= \frac{{\left( {x_1^2 - x_2^2} \right) - 3\left( {{x_1} - {x_2}} \right)}}{{{x_1} - {x_2}}} = \frac{{\left( {{x_1} + {x_2}} \right)\left( {{x_1} - {x_2}} \right) - 3\left( {{x_1} - {x_2}} \right)}}{{{x_1} - {x_2}}}\\
= \frac{{\left( {{x_1} - {x_2}} \right)\left( {{x_1} + {x_2} - 3} \right)}}{{{x_1} - {x_2}}} = {x_1} + {x_2} - 3\\
Vi\,{x_1},{x_2} > 2 \Rightarrow {x_1} + {x_2} - 3 > 0 \Rightarrow hs\,dong\,bien\,tren\,\left( {2; + \infty } \right)
\end{array}$
