Question 1029358
let a = the larger number
let b = the smaller number


a = 8b-2


this means that the larger number is 2 less than 8 times the smaller number.


a^2 - b^2 = 884.


this means that difference between the squares of each of the numbers is 884.


replace a^2 with (8b-2)^2 in the second equation to get:


(8b-2)^2 - b^2 = 884


simplify to get 64b^2 - 32b + 4 - b^2 = 884


combine like terms to get 63b^2 - 32b + 4 = 884


subtract 884 from both sides of this equation to get 63b^2 - 32b - 880 = 0


use the quadratic formula to get:


b = - 3.492063... or b = 4


the integer you are looking for is 4.


that's the smaller number


a = 8b-2 makes a = 30


that's the larger number.


a^2 - b^2 becomes (30)^2 - (4)^2 = 884.


the requirements are satisfied.


the larger number is 30.
the smaller number is 4.