Question

the product of two consecutive even integers is 528. find the integers.

Explanation:

Define variables for consecutive even integers

Using the Consecutive Integer Word Problems knowledge point
Let \(x\) be the smaller even integer.
The next consecutive even integer is \(x + 2\).

Set up the quadratic equation

Using the Consecutive Integer Word Problems knowledge point

$$ x(x + 2) = 528 $$

$$ x^2 + 2x - 528 = 0 $$

Solve the quadratic equation

Using the Solving Quadratic Equations knowledge point

$$ (x + 24)(x - 22) = 0 $$

$$ x = -24 \quad \text{or} \quad x = 22 $$

Determine the pairs of integers

Using the Consecutive Integer Word Problems knowledge point
If \(x = 22\), the integers are \(22\) and \(24\).
If \(x = -24\), the integers are \(-24\) and \(-22\).
Since standard consecutive integer problems typically seek positive integer solutions unless specified, we find the positive pair.
Smaller integer is \(22\).
Larger integer is \(24\).

Answer:

The product of two consecutive even integers is 528. Find the integers.

smaller integer = <blank>22</blank>

larger integer = <blank>24</blank>