Question 633892
Find three consecutive odd numbers such that the square of the second number
 is 192 less than the square of the third number.
:
Let x = the 1st integer, then (x+2) and (x+4) are the next two odd integers
:
Write an equation for the statement:
"the square of the second number is 192 less than the square of the third
 number."
(x+2)^2 = (x+4)^2 - 192
FOIL
x^2 + 4x + 4 = x^2 + 8x + 16 - 192
Combine the variables on the left
x^2 - x^2 + 4x - 8x = 16 - 192 - 4
:
-4x = -180
x = {{{(-180)/(-4)}}}
x = +45 is the 1st odd number
then
47 and 49 are the 2nd and 3rd odd digits
:
:
Check 
47^2 = 49^2 - 192
2209 = 2401 - 192