The sum of the squares of two numbers is 234 and the square of their difference is 144. Find the product of the two numbers?

Let the two numbers be x and y.
Then, x² + y² = 234 ...(i)
and (x - y)² = 144 ...(ii)
Now, (x - y)² = 144
⇒ x² + y² - 2xy = 144
⇒ 234 - 2xy = 144 [using Eq.(i)]
On substituting the value of x² + y² from Eq.(i) in Eq.(ii),
we get
2xy = 90
⇒ xy = 45
So, the product of the two numbers is 45.