# The product of two consecutive even integers is 624. How do you find the integers?

See a solution process below:

Therefore their product in standard form would be:

We can factor this as:

(x + 26)(x - 24) = 0

Solution 1:

Solution 2:

If the first number is 24 then the second number is:

There are two solutions to this problem:

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Let ( n ) represent the smaller of the two consecutive even integers. Then the next consecutive even integer is ( n + 2 ).

Since the product of the two consecutive even integers is 624, we can set up the equation:

[ n \cdot (n + 2) = 624 ]

Expanding the left side of the equation:

[ n^2 + 2n = 624 ]

Rearranging the equation into standard quadratic form:

[ n^2 + 2n - 624 = 0 ]

Now, we can solve this quadratic equation using factoring, completing the square, or the quadratic formula.

For simplicity, let's use factoring:

[ (n + 26)(n - 24) = 0 ]

This gives us two possible solutions:

- ( n + 26 = 0 ) --> ( n = -26 ) (not valid for consecutive even integers)
- ( n - 24 = 0 ) --> ( n = 24 )

So, the smaller of the two consecutive even integers is 24, and the next consecutive even integer is ( 24 + 2 = 26 ). Therefore, the two consecutive even integers are 24 and 26.

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