The sum of the squares of two numbers is 97 and the squares of their difference is 25. The product of the two numbers is:

The sum of the squares of two numbers is 97 and the squares of their difference is 25. The product of the two numbers is:
Answer: 36

Let numbers be (a) and (b). Given (a^2 + b^2 = 97), ((a - b)^2 = 25). Thus, (a - b = 5). Also, (a^2 + b^2 = (a - b)^2 + 2ab = 25 + 2ab = 97), so (2ab = 72), (ab = 36). Studying this highlights algebraic problem-solving, providing lessons on logical reasoning for mathematical solutions.