Let the two numbers be $x$ and $y$.

From the problem, we have two equations:

1. $x + y = 17$
2. $x \cdot y = 72$

To solve this, we can express $y$ in terms of $x$ from the first equation: $y = 17 - x$

Now, substitute $y$ in the second equation: $x \cdot (17 - x) = 72$

Expanding and rearranging terms: $x^2 - 17x + 72 = 0$

This is a quadratic equation. We can solve it using the quadratic formula: $x = \frac{-(-17) \pm \sqrt{(-17)^2 - 4 \cdot 1 \cdot 72}}{2 \cdot 1}$ $x = \frac{17 \pm \sqrt{289 - 288}}{2}$ $x = \frac{17 \pm \sqrt{1}}{2}$ $x = \frac{17 \pm 1}{2}$

So, we have two possible values for $x$:

1. $x = \frac{17 + 1}{2} = 9$
2. $x = \frac{17 - 1}{2} = 8$

If $x = 9$, then $y = 17 - 9 = 8$. If $x = 8$, then $y = 17 - 8 = 9$.

Thus, the two numbers are 8 and 9.

Would you like more details or have any questions?

Here are some related questions for further practice:

1. Find two numbers such that their sum is 20 and their product is 96.
2. If the sum of two numbers is 18 and their product is 77, what are the numbers?
3. Solve for two numbers where the sum is 12 and the product is 35.
4. Find two numbers with a sum of 24 and a product of 143.
5. If two numbers sum to 15 and their product is 54, what are the numbers?

Tip: For problems like this, express one variable in terms of the other using one equation, then substitute into the other to reduce it to a single-variable equation.