This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
The two numbers are 8 and 9. Steps: 1. Let the two numbers be x and y. 2. From the problem statement, we have two equations: x · y = 72 (Product) x + y = 17 (Sum) 3. From the second equation, express y in terms of x: y = 17 - x 4. Substitute this expression for y into the first equation: x · (17 - x) = 72 17x - x^2 = 72 5. Rearrange the terms to form a standard quadratic equation: x^2 - 17x + 72 = 0 6. Factor the quadratic equation. We need two numbers that multiply to 72 and add to -17. These numbers are -8 and -9. (x - 8)(x - 9) = 0 7. Solve for x: x - 8 = 0 x = 8 x - 9 = 0 x = 9 8. Find the corresponding y values using y = 17 - x: If x = 8, then y = 17 - 8 = 9. If x = 9, then y = 17 - 9 = 8. Both pairs (8, 9) and (9, 8) satisfy the conditions. Therefore, the two numbers are 8 and 9.