Question

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

Answer 1

12 and 14

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.

`(x+2)^2-x^2=52\\\\x^2+4+4x-x^2=52\\\\4+4x=52\\\\4x=52-4\\\\4x=48\\\\x=12`

First integer = 12

Another integer = 12+2 = 14