Question

If the sum of two numbers is 42 and their product is 437, then find the absolute difference between the numbers.

• A. 4
• B. 6
• C. 8
• D. 10

Answer 1

The Correct Option is A

Step 1: Define the numbers

Let the two numbers be \( x \) and \( y \). 

Step 2: Use the given conditions

\[ x + y = 42 \] \[ xy = 437 \]

Step 3: Apply the identity for the difference of squares

\[ (x - y)^2 = (x + y)^2 - 4xy \]

Step 4: Substitute the given values

\[ (x - y)^2 = 42^2 - 4 \times 437 \] \[ = 1764 - 1748 = 16 \]

Step 5: Solve for \( x - y \)

\[ x - y = \sqrt{16} = 4 \]

Thus, the absolute difference between the numbers is 4.