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The two consecutive positive even integers are [[1]] and [[2]] whose product is 288.

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answer is 16, 18.

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Detailed Solution

The two consecutive positive even integers are 16 and 18 whose product is 288.
Given that the product of two consecutive even integers are 288.
Let’s assume that

n

and

n + 2

are the two consecutive positive integers.
According to the given condition,

⟹ n (n + 2) = 288

⟹ n^{2} + 2 n = 288

⟹ n^{2} + 2 n - 288 = 0

⟹ n^{2} + 18 n - 16 n - 288 = 0

⟹ n (n + 18) - 16 (n + 18) = 0

⟹ (n - 16) (n + 18) = 0

⟹ n - 16 = 0 or n + 18 = 0

∴ n = 16 or n = - 18

We will choose the value

n = 16

because the product is of two positive integers.
So,

n = 16

∴ n + 2 = 16 + 2 = 18

Therefore, the integers are 16 and 18.

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