Question

The difference of two positive integers is 3 and the sum of their squares is 117; what are the numbers?

Answer 1

Answer:

6 & 9

Step-by-step explanation:

a and b are the two integers

1. a-b=3

2. a^2+b^2=117

(a-b)^2=3^2 => a^2+b^2-2ab=9 => 117-2ab=9 => 2ab=108 => ab=54

a=b+3-->  ab=54 => b(b+3)=54 => b^2+3b-54=0, b=-9(excluded as negative) & b=6

So we get b=6 and a=9