Question

Two numbers are such that their difference, their sum, and their product are in the ratio 1 : 4 : 15. What are the two numbers?

Answer 1

(a-b):(a+b):ab = 1:4:15

(a-b)/(a+b) = 1/4
4a-4b = a+b
3a = 5b

(a-b)/ab = 1/15
15a-15b = ab
15a-9a = a(3a/5)
30a = 3a^2
a = √10
b = 3/5 √10

15a+15b = 4ab
15a + 9a = 4a(3a/5)
120a = 12a^2
a = √10

a-b = 2/5 √10
a+b = 8/5 √10
ab = 6 = 30 * 2/5 √10

Dang! Doesn't work out at the end.
15(a-b) = 6√10, not just 6

Where's my mistake?