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Q.

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

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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,
⟹nn+2=288
⟹n2+2n=288
⟹n2+2n-288=0
⟹n2+18n-16n-288=0
⟹nn+18-16n+18=0
⟹n-16n+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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