SOLUTION: The sum of the squares of two consecutive positive even integers is 340. What are the integers? The answer should be in this form: 6 and 7

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Let the first positive even integer = x, then the next consecutive positive even integer = (x+2)
Simplify the left side.

Subtract 340 from both sides of the equation.
Factor a 2 from the left side.
Factor the parentheses.
Apply the zero product principle.
and/or
If then This is the first postive even integer.
If then Discard this solution as you want positive integers only.

The two integers are: 12 and 14
Check:
= 340