<PRE><B>Question 1095691</B>
let a be the larger number
let b be the smaller number


a - b = 3


a^2 - b^2 = 81


since a^2 - b^2 is equal to (a - b) * (a + b), then:


(a - b) * (a + b) = 81


since a - b = 3, then:


3 * (a + b) = 81


since a - b = 3, then a = b + 3 then:


3 * (a + b) = 81 becomes 3 * (b + 3 + b) = 81


simplify to get 3 * (2b + 3) = 81


simplify further to get 6b + 9 = 81


solve for b to get b = (81 - 9) / 6 = 12


since a = b + 3, then a = 15


your larger number is 15 and your smaller number is 12.


15 - 12 = 3


15^2 - 12^2 = 225 - 144 = 81


your solution is that the two number are 15 and 12.


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