We're given two pieces of information about two numbers, so let's call them x and y:

- The difference between x and y is 9: x - y = 9
- The sum of the squares of x and y is 153: x^2 + y^2 = 153

To solve for the values of x and y, we can start by solving the first equation for x:

x - y = 9  -->  x = 9 + y

Then we can substitute that expression for x into the second equation:

(9 + y)^2 + y^2 = 153

Expanding the squared term and simplifying gives:

2y^2 + 18y - 72 = 0

Dividing by 2 yields:

y^2 + 9y - 36 = 0

Which factors as:

(y + 12)(y - 3) = 0

So y = -12 or y = 3. Since we know x > y, it must be the case that y = 3 and x = 9 + y = 12. Finally, to answer the original question, we can compute the product of the two numbers: x * y = 12 * 3 = 36.
### Instruction:
The difference between two numbers is 9, and the sum of the squares of each number is 153. What is the value of the product of the two numbers?

### Response:
