The two consecutive even numbers whose product is 624 are 24 and 26.
Here's how to find them:
- Set up an equation: Let the first even number be x. The next consecutive even number is x + 2. The product of these numbers is 624. So, we have the equation: x(x + 2) = 624.
- Solve the equation: Expand the equation to get x² + 2x = 624. Rearrange to get x² + 2x - 624 = 0. This is a quadratic equation that can be factored into (x + 26)(x - 24) = 0. Therefore, the possible solutions are x = -26 or x = 24.
- Choose the positive solution: Since we are looking for even numbers, we discard the negative solution and take x = 24. The next consecutive even number is x + 2 = 26.
Therefore, the two consecutive even numbers whose product is 624 are 24 and 26.
