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. \( 10 \)
• E.

Hint:

To find the absolute difference between two numbers when their sum and product are known, use the difference of squares formula.

Answer 1

The Correct Option is A

Let the two numbers be \( x \) and \( y \). From the given conditions: \[ x + y = 42 \quad \text{and} \quad xy = 437 \] Step 1: Using the identity for the difference of squares: \[ (x - y)^2 = (x + y)^2 - 4xy \] Step 2: Substitute the known values: \[ (x - y)^2 = 42^2 - 4 \times 437 \] \[ (x - y)^2 = 1764 - 1748 = 16 \] Step 3: Taking the square root on both sides: \[ x - y = \sqrt{16} = 4 \] Thus, the absolute difference between the two numbers is \( \boxed{4} \).