If the sum of the cubes of two numbers is 72 and the difference of their squres is 12. Find the numbers.

Answer 1

x^3 + y^3 = 72
x^2 - y^2 = 12

We could just do this by listing the cubes less than 72 :
1, 8, 27, 64

the only combination for a sum of 72 is 8 + 64
so x=2, y=4

so the numbers are 2 and 4

is the difference property ok?
is 16-4 = 12 ?? YES

Answer 2

also, we have
(x+y)(x-y) = 12
The pairs of factors of 12 are
1,12 2,6 3,4

x+y=6
x-y=2
x=4,y=2