Question

Three consecutive even integers are such that the square of the third is 76 more than the square of the second. How do you determine the three integers?

Answer 1

16, 18, and 20.

Explanation:

One can express the three consecuitve even numbers as `2x, 2x+2, and 2x+4`. You are given that `(2x+4)^2 = (2x+2)^2 +76`. Expanding the squared terms yields `4x^2+16x+16 = 4x^2+8x+4+76`.
Subtracting `4x^2+8x+16` from both sides of the equation yields `8x=64`. So, `x=8`. Substituting 8 for x in `2x, 2x+2, and 2x+4`, gives 16,18, and 20.