Question

The sum of two numbers is 15 and the sum of their squares is 113. The product of the two numbers is:

• A. 56
• B. 48
• C. 60
• D. 52

Answer 1

The Correct Option is A

Step 1: \((a+b)^2 = a^2 + b^2 + 2ab \Rightarrow 15^2 = 113 + 2ab\).
Step 2: \(225 - 113 = 2ab \Rightarrow ab = \dfrac{112}{2} = 56\).

Quick Tip: Use \(2ab=(a+b)^2-(a^2+b^2)\) to get the product without finding the numbers.