Question

One number is 3 more than another. The difference between their square is 63. What are the numbers?

Answer 1

x = y + 3
x^2 - y^2 = 63

(y + 3)^2 - y^2 = 63
(y + 3)(y + 3) - y^2 = 63
y^2 + 6y + 9 - y^2 = 63
6y + 9 = 63
6y = 54
y = 54/6
y = 9

x = y + 3
x = 9 + 3
x = 12

check...
x^2 - y^2 = 63              x = y + 3
12^2 - 9^2 = 63           12 = 9 + 3
144 - 81 = 63               12 = 12 (correct)
63 = 63 (correct)

ur 2 numbers are 9 and 12