65. Find two numbers whose sum is 20 and product is 96.
65. Diophantus' Solution. Let $2 n$ be the difference between the two numbers. Then the larger one is $10+n$, and the smaller one is 10 - $n$. The product is $100-n^{2}=96 ; n^{2}=4$ and $n=2$. The required numbers are 12 and 8.