The ratio of two numbers is 3 to 2 and the difference of their squares is 20. Find the numbers.
a/b = 3/2 so a is bigger
a^2 - b^2 = 20
well
b = 2a/3
so
a^2 - 4a^2/9 = 20
9 a^2 - 4 a^2 = 180
a^2 = 36
a = 6 or -6
try a = 6
then b = 4
36 - 16 = 20 sure enough
then also check a = -6
then b = -4
36 - 16 = 20 so that works too