The sum of the squares of two positive integers is 193. The product of the two integers is 84. What is the sum of the two integers?

(a+b)^2=a^2+b^2+2ab

=193+2*84

=361

a+b=19

A * B = 84, 
A^2 + B^2 = 193, solve for A, B 
Use substitution and you get:
A = 12  and  B = 7
Sum = 12 + 7 = 19