If the number x is 3 less than the number y and the sum of the squares of x and y is 29, find the product of x and y.

Given,

x = y - 3 or x - y = -3 and

x² + y² = 29.

We know that,

(x - y)² = x² + y² - 2xy

Putting values of x - y and x² + y² we get,

(-3)² = 29 - 2xy

⇒ 2xy = 29 - 9

⇒ 2xy = 20

⇒ xy = 10

Hence, xy = 10.