Answer:
12, 14
Explanation:
Let x = smaller positive even integer.
Then x + 2 is the next greater even integer.
Add the squares of the numbers.
x² + (x + 2)²
Set the sum equal to 340.
x² + (x + 2)² = 340
x² + x² + 4x + 4 = 340
2x² + 4x - 336 = 0
x² + 2x - 168 = 0
We need to factor the left side. We need 2 factors of -168 that add to 2.
168 = 2³ × 3 × 7
2² × 3 = 12
2 × 7 = 14
14 × (-12) = -168
14 + (-12) = 2
The factors are 14 and -12.
x² + 2x - 168 = 0
(x - 12)(x + 14) = 0
x - 12 = 0 or x + 14 = 0
x = 12 or x = -14
x = 12
x + 2 = 12 + 2 = 14
Answer: 12, 14