Question

What are the consecutive even integers whose product is 48?

a) 6, 8
b) 4, 12
c) 2, 24
d) 10, 5

Answer 1

The consecutive even integers around the square root of 48 are 6 and 8, and their product is indeed 6 × 8 = 48. Therefore, the correct answer is (a) 6, 8.

Step-by-step explanation:

The question asks to find the consecutive even integers whose product is 48. To find these numbers, we can note that the square root of 48 is between 6 and 7, so our consecutive even integers must be around these numbers. To find consecutive even integers whose product is 48, we can start by listing the even integers and their products:

2 * 24 = 48

4 * 12 = 48

6 * 8 = 48 The consecutive even integers around the square root of 48 are 6 and 8, and their product is indeed 6 × 8 = 48. Therefore, the correct answer is (a) 6, 8.

Answer 2

The consecutive even integers whose product is 48 are 6 and 8, found by factoring the quadratic equation derived from setting up the product of two consecutive even integers equal to 48.

Step-by-step explanation:

To find the consecutive even integers whose product is 48, we can set up a simple equation. If we call the smaller integer 'n', then the next consecutive even integer would be 'n + 2'. Thus, the product of these two numbers is n(n + 2) = 48. We can solve this quadratic equation to find the value of 'n'.

Let's solve the equation step by step:

1. Write the equation: n(n + 2) = 48
2. Expand the equation: n2 + 2n = 48
3. Subtract 48 from both sides: n2 + 2n - 48 = 0
4. Factor the quadratic: (n + 8)(n - 6) = 0
5. Solve for 'n': n = -8 or n = 6

Since we are looking for even integers, the negative solution does not fit the context of the problem. Therefore, the consecutive even integers we are seeking are 6 and 8.

Answer: The consecutive even integers whose product is 48 are 6 and 8, which corresponds to option (a).