The sum of the squares of two consecutive positive even integers is 52.find the integers

The two consecutive positive integers are and .

Step-by-step explanation:

Let be an even integer, then the next even integer is .

The sum of the squares of these even integers is .

We can write the following equation and solve for .

.

We expand to get,

.

We simplify to get,

.

This gives us,

We divide through by 2 to get,

.

This is now a quadratic trinomial

We split the middle term to get,

.

We factor to obtain,

We discard since it is not a positive integer.

Hence the two consecutive positive even integers are,

and

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