Question

If the sum of two numbers is 14 and their difference is 10, find the product of these two numbers

• A. 18
• B. 20
• C. 24
• D. 22

Hint:

$ab = \frac{(a+b)^2 - (a-b)^2}{4} = \frac{196 - 100}{4} = 24$.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Algebraic identities relate the product of two numbers to their sum and difference.

Step 2: Key Formula or Approach:
Let the two numbers be $a$ and $b$.
Given $a + b = 14$ and $a - b = 10$.
Adding both equations:
\[2a = 24 \implies a = 12\] Subtracting the equations:
\[2b = 4 \implies b = 2\]

Step 3: Detailed Explanation:
Product of the two numbers:
\[a \times b = 12 \times 2 = 24\] Alternatively, using the identity $ab = \frac{(a+b)^2 - (a-b)^2}{4} = \frac{14^2 - 10^2}{4} = \frac{196 - 100}{4} = 24$.

Step 4: Final Answer:
Therefore, the product of the two numbers is 24.