1.1.1. (2 points) Find the sum of the squares of two numbers if it is known that their arithmetic mean is 8, and the geometric mean is $2 \sqrt{5}$.
Answer: 216.

Solution. If $a$ and $b$ are the numbers in question, then $a+b=16, a b=(2 \sqrt{5})^{2}=20$, therefore

$$
a^{2}+b^{2}=(a+b)^{2}-2 a b=256-40=216 .
$$