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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?

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Surely by mistake. You seem to be having a run of mistakes in your sources. – Gerry Myerson Jul 11 '12 at 4:49
Is it $36$ or $136$? – user17762 Jul 11 '12 at 4:50
A^2 - B^2 =36 so A=10 , B=8 OR Marvis's comment – Zeta.Investigator Jul 11 '12 at 4:55
The answer to the problem as written is not $10$. The only possibility is $36=6^2+0^2$. – André Nicolas Jul 11 '12 at 12:47

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 $$A = ±6,\quad B = ±10.$$

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