document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=978538>Question 978538</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (a+b square root 2) (a-b square root 2)  <BR>\n" );
document.write( "Prove that this is an integer a,b are integers\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #599911 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=599911\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left(a\ +\ b\sqrt{2}\right)\left(a\ -\ b\sqrt{2}\right)\">\r<BR>\n" );
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document.write( "Is the product of two conjugates.  The product of two conjugates is the difference of two squares.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left(\sqrt{2}\right)^2\ =\ 2\">\r<BR>\n" );
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document.write( "by definition of square root, and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 2\ \in\ \mathbb{Z}\"> by definition of Integer.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ a\ \in\ \mathbb{Z}\ \Right\ a^2\ \in\ \mathbb{Z}\">,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ b\ \in\ \mathbb{Z}\ \Right\ b^2\ \in\ \mathbb{Z}\">,\r<BR>\n" );
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document.write( "and\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ b^2, 2\ \in\ \mathbb{Z}\ \Right\ 2b^2\ \in\ \mathbb{Z}\">\r<BR>\n" );
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document.write( "by Closure of Integer Multiplication.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ a^2,\, 2b^2\ \in\ \mathbb{Z}\ \Right\ a^2\ -\ 2b^2\ \in\ \mathbb{Z}\">\r<BR>\n" );
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document.write( "by Closure of Integer Subtraction.\r<BR>\n" );
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document.write( "Q.E.D.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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