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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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    The answer to the problem as written is not $10$. The only possibility is $36=6^2+0^2$.2012-07-11

1 Answers 1

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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 $A = ±6,\quad B = ±10.$