I am having trouble with the following question
If A and B are positive integers and $A^2 + B^2 = 36$ Then what is $A$? The choices are 6, 7, 8, 9, or 10.
How does one show that answer is 10?
The only possible (integer) solutions are: $$A = 0,\quad B= ±6$$ or $$A = ±6,\quad B= 0.$$
If the question would have been $A^2+B^2 = 136$ on the other hand, then the solutions would be: $$A = ±10,\quad B = ±6$$ and $$A = ±6,\quad B = ±10.$$