Question

The difference of the square 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

Integers are 12 and 14

Explanation:

Let the given consecutive even integers be X and X+2

Now

Given as the difference of the square of two positive consecutive integers is 52

i.e (X+2)² - x² = 52

or (X²+4x+4) - X² = 52

or X²+4x+4-X² = 52

or 4x+4 = 52

or x+1 =
`(52)/(4)`

x= 13 - 1

i.e X = 12

and X+2 = 12+2 = 14

so, positive consecutive integers are 12 and 14 ( Answer )