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?

1 Answer
Jan 27, 2016

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.