Final answer:
To find the three consecutive even integers, use the given equation 2x + (x + 2) = 268226. By solving this equation, we find that the three integers are 89408, 89410, and 89412.
Step-by-step explanation:
To find the three consecutive even integers, let's represent the first even integer as x.
The second consecutive even integer can be represented as (x + 2), and the third consecutive even integer can be represented as (x + 4). We are given that twice the first integer added to the second is 268226.
So, we can write the equation as 2x + (x + 2) = 268226. Solving this equation will help us find the value of x and subsequently, the three integers.
Combining like terms, we get 3x + 2 = 268226. Subtracting 2 from both sides gives us 3x = 268224. Dividing both sides by 3 gives us x = 89408.
Therefore, the three consecutive even integers are 89408, 89410, and 89412.