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The difference of the squares of two positive consecutive even integers is 52. Find the integers. Use the fact that, if x represents an even integer, then x + 2 represents the next consecutive even integer

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Answer:

12 and 14

Step-by-step explanation:

Let x represents an even integer. Another positive consecutive even integer will be (x+2).

According to question,

The difference of the squares of two positive consecutive even integers is 52 i.e.

[tex](x+2)^2-x^2=52\\\\x^2+4+4x-x^2=52\\\\4+4x=52\\\\4x=52-4\\\\4x=48\\\\x=12[/tex]

First integer = 12

Another integer = 12+2 = 14

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