Let $\#$ be the relation defined by $A \# B = A^2 + B^2$. If $A \# 5 = 169$, what is the positive value of $A$?
I need to find a positive number $A$ such that $A^2 + 25 = 169$. I can rearrange this equation to get $A^2 = 144$. Taking the square root of both sides, I get $A = \pm 12$. Since I want the positive value of $A$, I can ignore the negative one and conclude that $A = 12$. 