9.2. The number $a$ is a root of the quadratic equation $x^{2}-x-50=0$. Find the value of $a^{3}-51 a$.
Answer: 50. Solution. We have $a^{2}=a+50$, therefore $a^{3}=a^{2}+50 a=a+50+50 a=51 a+50$. Hence $a^{3}-51 a=50$.