The product of two consecutive even numbers is 2208.what is the greater number?Options4852465456

The problem is asking for two consecutive even numbers that multiply to 2208.

Step 1: Let's denote the smaller even number as x. Then the next consecutive even number would be x + 2.

Step 2: We know that the product of these two numbers is 2208, so we can set up the equation: x * (x + 2) = 2208.

Step 3: This simplifies to x^2 + 2x - 2208 = 0.

Step 4: This is a quadratic equation, and we can solve it by factoring, completing the square, or using the quadratic formula. The factored form of the equation is (x - 46)(x + 48) = 0.

Step 5: Setting each factor equal to zero gives the solutions x = 46 and x = -48.

Step 6: Since we're looking for a positive even number, we discard the negative solution. So, the smaller even number is 46.

Step 7: The next consecutive even number (which is the greater number we're looking for) is 46 + 2 = 48.

So, the greater number is 48.