10.2. The number $a$ is a root of the quadratic equation $x^{2}-x-50=0$. Find the value of $a^{4}-101 a$.
Answer: 2550. Solution. We have $a^{2}=a+50$, therefore $a^{4}=(a+50)^{2}=a^{2}+100 a+2500=$ $a+50+100 a+2500=101 a+2550$. Hence $a^{4}-101 a=2550$.