9.2. The number $a$ is a root of the quadratic equation $x^{2}-x-100=0$. Find the value of $a^{4}-201 a$
Answer: 10100.

Solution. Squaring the expression $a^{2}=a+100$, we get $a^{4}=a^{2}+200a+10000=a+100+200a+10000=201a+10100$. From this, we obtain the answer.