Question 1027956
let a be the larger number.
let b be the smaller number.


you get:


a - b = 6
a^2 - b^2 = 60


in the first equation, solve for a to get a = b + 6


in the second equation, replace a with (b+6) to get:


(b+6)^2 - b^2 = 60


simplify to get:


b^2 + 12b + 36 - b^2 = 60


combine like terms to get:


12b + 36 = 60


subtract 36 from both sides of this equation to get:


12b = 24


solve for b to get:


b = 2


if b = 2, the a - b = 6 becomes a - 2 = 6


add 2 to both sides of this equation to get a = 8


when a = 8 and b = 2, you get:


a - b = 8 - 2 = 6
a^2 - b^2 = 8^2 - 2^2 = 64 - 4 = 60


this confirms the solution is correct.


the numbers are 8 and 2.


subtract the smaller number from the larger number and you get 6.


subtract the square of the smaller number from the square of the larger number and you get 60.