If b is an integer .... Please help

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If b is an integer .... Please help

by moonlite » Mon Jun 09, 2008 12:30 pm
If b is an integer, is sqrt a^2 +b^2 an integer? (sqrt is over a^2 +b^2)

1) a^2 +b^2 is an integer
2) a^2 - 3b^2 = 0

OA B

Please explain thanks.

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by netigen » Mon Jun 09, 2008 12:40 pm
a^2 - 3b^2 = 0

or a^2 = 3b^2

a^2 + b^2 = 3b^2 + b^2 = 4b^2

sqrt(4b^2) = 2b

as we know b is an integer

so B is sufficient.

Also, A just tells us that a^2 is an integer so insufficient.