The sum of the squares of two numbers is 97, and the square of their difference is 25. What is the product of the two numbers?
Q1. The sum of the squares of two numbers is 97, and the square of their difference is 25. What is the product of the two numbers?
Answer: 36
Explanation: Given a²+b²=97 and (a−b)²=25: expanding gives a²−2ab+b²=25, so 97−2ab=25, thus ab=36. Show the calculation clearly when solving similar quantitative items.