Question 82755
Three consecutive even integers are such that the square of  the third is 76 more than the square of the second. Find the three integers. 
:
Let x = 2nd consecutive number
Then (x+2) = 3rd consecutive number
:
"the third is 76 more than the square of the second." which can be written:
(x+2)^2 = 76 + x^2
:
x^2 + 4x + 4 = x^2 + 76
:
x^2 - x^2 + 4x = 76 - 4
:
4x = 72
:
x = 72/4
:
x = 18 is the 2nd even consecutive number
:
16, 18, 20 are the numbers
:
Check on a calc: 20^2 - 18^2 = 76