Question

The product of two consecutive positive even integers is 440. What are the integers?

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Answer 1

if intergers are n and n+2 we have the equation

n(n + 2) = 440
n^2 + 2n - 440 = 0
(n - 20)(n + 22) = 0

n = 20 , -22 (ignore the -22 because the integers are positive)

So the integers are 20,22

Answer 2

If the average of the two integers is x, the product of the two integers is
(x-1)(x+1) = 440
x² - 1 = 440
x² = 441 = 21²

21 is the odd integer between the two even integers you seek.

The integers are 20 and 22.