Question

The sum of two numbers is 10 and the sum of their squares is 68. Find the product of the numbers.

Answer 1

Given:

• The sum of two numbers x and y is 10, i.e., x + y = 10.
• The sum of their squares is 68, i.e., x² + y² = 68.

Step-wise calculation:

1. Start from the square of the sum:

(x + y)² = 10²

(x + y)² = 100

Expanding the left side:

x² + y² + 2xy = 100

2. Substitute x² + y² = 68:

68 + 2xy = 100

3. Solve for the product xy: 

2xy = 100 – 68

2xy = 32

xy = `32/2`

xy = 16

The product of the two numbers is 16.