Question

The difference of the squares of two positive consecutive even integers is 36. Find the integers. Use the fact that, if x represents an even integer, then x+2 represents the next consecutive even integer.

Answer 1

Hello from MrBillDoesMath!

Answer:

8 and 10

Discussion:

Let x and x+2 be as described in the Question. Then

(x+2)^2 - x^2 = 36 => (x+2)^2 = x^2 + 2x + 4

x^2 + 4x + 4 - x^2 =36 => the x^2 terms cancel

4x + 4 = 36 => subtract 4 from both sides

4x = 36 -4 - 32 => divide both sides by 4

x = 32/4 = 8

So the integers are 8 and 10 (8+2)

Check: 10^2 - 8^2 = 100 -64 - 36.

Thank you,

MrB