Question

The difference of the squares of two positive consecutive even integers is 4444. find the integers. use the fact​ that, if x represents an even​ integer, then xplus+2 represents the next consecutive even integer.

Answer 1

Remember that the formula for the difference of squares is $a^2 - b^2$, where $a$ and $b$ are expressions or values.

In this case, we have two expressions, $x$ and $(x + 2)$. We are also given that their difference of squares is 4444. Using the formula, we can say:

$(x + 2)^2 - x^2 = 4444$

Now, we can solve for $x$:

$(x + 2)^2 - x^2 = 4444$

$(x^2 + 4x + 4) - x^2 = 4444$

$4x + 4 = 4444$

$4x = 4440$

$x = 1110$

We now know that the first number is 1110. To find the second number, we must add 2 to the first number, which means that the second number, represented by $(x + 2)$, is equal to 1112.

Our two numbers are 1110 and 1112.